JP2007101374A - Measuring instrument and measuring method using gas adsorption - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To allow precise measurement, to allow a wide range of measurement free from selection of a measuring condition, to facilitate analysis, and to obtain a high S/N ratio. <P>SOLUTION: A sample chamber is constituted using a microchannel. A volume modulation means modulates a volume of the sample chamber. A pressure measuring means measures pressure in the sample chamber. An analytical means carries out analysis based on a response characteristic of the pressure measured by the pressure measuring means with respect to the modulation of the volume by the volume modulation means. The volume modulation means modulates the volume of the sample chamber. The pressure measuring means measures the pressure in the sample chamber. A volume control means feedback-controls the volume modulation means, based on the pressure measured by the pressure measuring means. The analytical means carries out the analysis based on the response characteristic of the pressure measured by the pressure measuring means with respect to the modulation of the volume by the volume modulation means. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a measuring apparatus and a measuring method for measuring a sample in a sample chamber using a phenomenon of gas adsorption.

  A gas adsorption method is generally used to measure the pore distribution. In this method, after putting a sample into a sample cell and degassing the sample cell, the adsorption amount of nitrogen gas is measured at the liquid nitrogen temperature, and the pore distribution is obtained based on the adsorption amount.

  Further, an FR (Frequency Response) method is known as a method for measuring the pore distribution. In this method, a vacuum chamber and a gas manifold are used, and the sample chamber is filled with gas molecules to be measured and sealed. Thereafter, the volume of the space sealed by the bellows is modulated with a sine wave, and the pressure at that time is measured. From the change in the pressure amplitude with respect to the volume change and the delay in the phase of the pressure amplitude, the diffusion rate of the molecules in the sample pore can be measured, and the cross-sectional area and volume of the pore can be calculated by further analysis.

The principle of analysis is
(1) When the speed of diffusion coincides with the speed of modulation, the delay in pressure phase becomes maximum, so that the diffusion speed can be understood.
(2) The diffusion rate differs depending on the pore diameter, and therefore the frequency at which the phase delay is maximum also differs. If the gas is known, the pore diameter can be determined.
(3) If the modulation is faster, the effect of volume modulation will not be transmitted to the inside of the pores. Conversely, if the diffusion is faster, the pressure change will be transmitted to all the inside of the pores. Can be calculated.
That's it.

The BET method is often used as a method for measuring the size distribution of pores, but the FR method is superior to the BET method in that it can be measured dynamically using the types of molecules actually involved in the reaction. And points that can be measured at any temperature.
Kazuhiro Sugao “Specific surface area / pore distribution measurement by gas adsorption method” Shimadzu review Vol. 48 No. 1 (1991) p35-49 J. et al. Phys. Chem. B 1997, 101, 614-622

When measuring the pore distribution by the gas adsorption method, it is conceivable to use a microchannel instead of the sample cell or the sample chamber in order to improve the efficiency of the measurement. For example, when measuring the pore distribution of a catalyst, there are the following methods for introducing the catalyst into the microchannel.
(1) The catalyst is filled in the channel.
(2) The catalyst is attached to the channel wall via the carrier.
(3) The catalyst is adhered to the channel wall surface using the channel wall as a carrier.
(4) The microchannel structure itself is formed of a catalyst.

  However, in the methods (1) and (2), it is difficult to accurately control the amount of catalyst in the channel. In addition, even if it is attempted to measure the introduction amount by weight measurement after introduction, the weight of the microchannel device is much larger than that of the sample and cannot be accurately measured.

  In the above methods (3) and (4), the microchannel device is a measurement target, but the conventional apparatus can obtain only the measurement results not only on the inside of the channel but also on the entire surface of the structure. In the adsorption method, it is necessary to keep the entire sample at the liquid nitrogen temperature. However, if the sample chamber is enlarged, there is a restriction on the apparatus side that it is difficult to maintain the liquid nitrogen temperature and high measurement accuracy cannot be obtained.

  One object of the present invention is to solve the above problems by using a microchannel for measurement by the FR method.

  In the FR method, since the volume (or the position of the bellows) is an input and the pressure in the sample chamber is an output, it is essentially non-linear (pressure and volume are inversely proportional), and analysis is difficult. In practice, the analysis is facilitated by conducting an experiment under a condition in which the volume variation is reduced so that the nonlinearity can be ignored (for example, 1 to 3% of the volume of the sample chamber).

  However, if the fluctuation is reduced, there is a problem that the signal intensity is reduced, the SN ratio is lowered, and the apparatus is enlarged to increase the substantial capacity of the sample chamber. In addition, since the signal intensity is low, considerations such as keeping the room temperature constant are necessary, and a high SN ratio cannot be obtained unless the installation environment is prepared.

  Another object of the present invention is to provide a measuring apparatus and a measuring method that are easy to analyze and can provide a high S / N ratio.

The measurement apparatus of the present invention is a measurement apparatus that performs measurement on a sample in a sample chamber using a phenomenon of gas adsorption, wherein the sample chamber is configured using a microchannel, and the measurement device has a volume of the sample chamber. A volume modulation means for modulating the pressure, a pressure measurement means for measuring the pressure in the sample chamber, and an analysis for performing an analysis based on a response characteristic of the pressure measured by the pressure measurement means with respect to a volume modulation by the volume modulation means And means.
According to this measuring apparatus, since the analysis based on the response characteristic of the pressure measured by the pressure measuring unit with respect to the volume modulation by the volume modulating unit is performed, the sample chamber is configured with high accuracy when configured using a microchannel. Measurement is possible, and a wide range of measurements can be performed regardless of the measurement conditions.

  The analysis means may analyze the pore distribution of the sample in the sample chamber.

  The sample chamber may be configured by connecting a microchannel of a detachable microchannel device that stores a sample and a microchannel on the measurement apparatus side to which the volume modulation unit is attached.

  The volume modulation means and the pressure measurement means may be attached to a member in which a microchannel on the measurement device side is formed.

  The pressure measuring means may be incorporated in the microchannel device.

  The volume modulation means may be configured using a piezoelectric element that modulates the volume of the sample chamber.

  The pressure measuring means may be configured using a semiconductor pressure sensor.

The measuring apparatus according to the present invention is a measuring apparatus that measures a sample in a sample chamber based on gas adsorption responsiveness, a volume modulation unit that modulates the volume of the sample chamber, and a pressure measurement that measures the pressure in the sample chamber. Means, feedback control of the volume modulation means based on the pressure measured by the pressure measurement means, and response of the pressure measured by the pressure measurement means to volume modulation by the volume modulation means An analysis means for performing an analysis based on the characteristics.
According to this measuring apparatus, the volume can be modulated while correcting the nonlinearity of the pressure at the time of measurement. Therefore, it is not necessary to consider the nonlinearity of the pressure, and the analysis based on the response characteristic of the pressure becomes easy. Further, since the modulation width can be increased, a high S / N ratio can be obtained.

  The volume control means may feedback control the volume modulation means so that the pressure measured by the pressure measurement means becomes a sine wave.

  The volume control means may feedback control the volume modulation means so that a product of a pressure measured by the pressure measurement means and a value obtained by differentiating the volume with respect to time becomes a sine wave.

The measurement method of the present invention is a measurement method for measuring a sample in a sample chamber based on gas adsorption responsiveness, the step of modulating the volume of the sample chamber, the step of measuring the pressure in the sample chamber, Feedback control of the modulation amount in the step of modulating the volume based on the pressure measured by the step of measuring pressure, and measuring the pressure relative to the modulation of the volume by the step of modulating the volume. And performing an analysis based on a response characteristic of the pressure.
According to this measurement method, the volume can be modulated while correcting the non-linearity of the pressure at the time of measurement. Therefore, it is not necessary to consider the non-linearity of the pressure, and the analysis based on the pressure response characteristic is facilitated. Further, since the modulation width can be increased, a high S / N ratio can be obtained.

  In the step of feedback controlling the modulation amount, the modulation amount in the step of modulating the volume may be feedback controlled so that the pressure measured in the step of measuring the pressure becomes a sine wave.

  In the step of feedback controlling the modulation amount, the modulation amount in the step of modulating the volume so that the product of the pressure measured in the step of measuring the pressure and a value obtained by time differentiation of the volume becomes a sine wave. May be feedback controlled.

  According to the measuring apparatus of the present invention, the analysis based on the response characteristic of the pressure measured by the pressure measuring unit with respect to the modulation of the volume by the volume modulating unit is performed. Therefore, when the sample chamber is configured using a microchannel, High-precision measurement is possible, and a wide range of measurements can be performed regardless of measurement conditions.

  According to the measuring device of the present invention, the volume can be modulated while correcting the nonlinearity of the pressure at the time of measurement. Therefore, it is not necessary to consider the nonlinearity of the pressure, and the analysis based on the response characteristic of the pressure is easy. Become. Further, since the modulation width can be increased, a high S / N ratio can be obtained.

  According to the measurement method of the present invention, the volume can be modulated while correcting the nonlinearity of the pressure at the time of measurement. Therefore, it is not necessary to consider the nonlinearity of the pressure, and the analysis based on the response characteristic of the pressure is easy. Become. Further, since the modulation width can be increased, a high S / N ratio can be obtained.

  FIG. 1 is a block diagram functionally showing the measuring apparatus of the present invention.

  In FIG. 1, a sample chamber 101 is configured using a microchannel. The volume modulation unit 102 modulates the volume of the sample chamber 101. The pressure measuring unit 103 measures the pressure in the sample chamber 101. The analysis unit 104 performs an analysis based on the response characteristic of the pressure measured by the pressure measurement unit 103 with respect to the volume modulation by the volume modulation unit 102.

  The volume modulation unit 111 modulates the volume of the sample chamber 101A. The pressure measuring unit 112 measures the pressure in the sample chamber 101. The volume control unit 113 feedback-controls the volume modulation unit 111 based on the pressure measured by the pressure measurement unit 112. The analysis unit 114 performs an analysis based on the response characteristic of the pressure measured by the pressure measurement unit 112 with respect to the volume modulation by the volume modulation unit 111.

  Here, the sample chamber 101A is not limited to a device dedicated to the apparatus or created for general use for measurement. Other containers attached via adapters also correspond to the sample chamber 101A. For example, depending on the purpose of measurement, a cell portion of a fuel cell, an exhaust gas purification catalyst unit of an automobile, and the like can be attached.

  Further, the configuration of the volume modulation means 111 is not limited. For example, a method using a bellows, a method using a piston, a method of deforming a wall by mechanical stress, and the like can be applied.

  The configurations of the pressure measuring unit 103 and the pressure measuring unit 112 are not limited. For example, a semiconductor pressure sensor can be used.

  The shape of the microchannel constituting the sample chamber 101 is not limited. The microchannel may be a channel having a diameter or width of 1 mm or less, may be linear, or may be bent to increase the length. The material constituting the microchannel and the size of the microchannel can be appropriately selected according to the purpose of measurement.

  Hereinafter, the measurement apparatus of Example 1 will be described with reference to FIGS. This embodiment shows an example in which the measuring apparatus of the present invention is applied to a catalyst evaluation apparatus.

  FIG. 2 is a cross-sectional view illustrating the configuration of the measurement apparatus according to the first embodiment.

  As shown in FIG. 2, the measuring apparatus of the present embodiment is configured to introduce the member 1 constituting the sample chamber, the connector 31 and the connector 32 for fixing the microchannel device 2, and the introduction and introduction of gas into the sample chamber. A valve 41 and a valve 42 for performing.

  The member 1 is formed with a microchannel 10 constituting a sample chamber, and the microchannel device 2 is formed with a microchannel 20 constituting a sample chamber and receiving a catalyst. As will be described later, the sample chamber is formed by connecting the microchannel 10 and the microchannel 20.

  As shown in FIG. 2, a piezoelectric element 11 made of a PZT thin film or the like for modulating the volume of the sample chamber and a semiconductor pressure sensor 12 for detecting the pressure in the sample chamber are attached to the member 1.

  FIG. 3 is a block diagram illustrating a configuration of a control system in the measurement apparatus according to the first embodiment.

  As shown in FIG. 3, the measuring apparatus of the present embodiment supplies gas to the sample chamber by operating a calculation unit 51 that receives a signal from the semiconductor pressure sensor 12 and performs analysis, a valve 41, a valve 42, and the like. A gas supply mechanism 52 that controls the piezoelectric element 11, the semiconductor pressure sensor 12, a calculation unit 51, and a control unit 53 that controls the gas supply mechanism 52.

  Next, a measurement method using the measurement apparatus of this example will be described.

First, a catalyst is introduced into the microchannel device 2. As a method of introducing the catalyst into the microchannel,
(1) The catalyst is filled in the channel.
(2) The catalyst is attached to the channel wall via the carrier.
(3) The catalyst is adhered to the channel wall surface using the channel wall as a carrier.
(4) The microchannel structure itself is formed of a catalyst.
Etc. can be adopted.

  Next, the microchannel device 2 is attached to the measurement apparatus via the connector 31 and the connector 32. Further, the member 1 and the microchannel device 2 are sandwiched between the valve 41 and the valve 42. Thereby, the microchannel 10 and the microchannel 20 are hermetically connected, and a sample chamber is formed.

  FIG. 4 is a flowchart showing a processing procedure at the time of measurement in the measurement apparatus of the present embodiment. This processing procedure is executed under the control of the control unit 53.

  After the airtight state is formed as described above, in step S1 of FIG. 4, a gas to be measured is introduced by the gas supply mechanism 52, and the sample chamber is replaced with this gas. Next, in step S2, introduction of gas is stopped and an airtight state is maintained.

  Next, in step S3, measurement by the FR method is performed. Here, the piezoelectric element 11 applies sinusoidal modulation to the volume of the sample chamber in an airtight state. When the piezoelectric element 11 is driven, the wall 11a of the member 1 facing the piezoelectric element 11 receives a stress and vibrates, thereby modulating the volume of the sample chamber. The pressure in the sample chamber is detected by the pressure sensor 12 while changing the frequency of the sine wave. The calculation unit 51 calculates the diffusion rate of molecules in the pores of the catalyst based on the change in pressure amplitude and the phase delay of the pressure change with respect to the volume change. Furthermore, the cross-sectional area and volume of the pore can be obtained by analysis in the calculation unit 51.

The principle of analysis is
(1) When the speed of diffusion coincides with the speed of modulation, the delay in pressure phase becomes maximum, so that the diffusion speed can be understood.
(2) The diffusion rate differs depending on the pore diameter, and therefore the frequency at which the phase delay is maximum also differs. If the gas is known, the pore diameter can be determined.
(3) If the modulation is faster, the effect of volume modulation will not be transmitted to the inside of the pores. Conversely, if the diffusion is faster, the pressure change will be transmitted to all the inside of the pores. Can be calculated.
That's it.

  When the process of step S3 ends, the series of processes shown in FIG. 4 ends.

  In the measuring apparatus of the present embodiment, a configuration in which the volume is modulated while correcting the nonlinearity of the pressure at the time of measurement (step S3 in FIG. 4) can be applied by controlling the piezoelectric element 11 by feedback control. According to such a method, since the nonlinearity is corrected by the volume corresponding to the input side, it is not necessary to consider the nonlinearity for the pressure corresponding to the output side even if the modulation width is increased, and the analysis in the calculation unit 51 is easy. Become.

The method for controlling the piezoelectric element 11 is one of the following methods.
(1) The piezoelectric element 11 is feedback-controlled so that P becomes a sine wave.
(2) The piezoelectric element 11 is feedback-controlled so that P · (dv / dt) becomes a sine wave. However, “P” is the pressure in the sample chamber, and “v” is the volume of the sample chamber.

  In the method (1), the nonlinearity is corrected by controlling so as to directly remove the distortion of the pressure P due to the nonlinearity.

In the method (2), considering a short time δt in which the change in the pressure P can be ignored,
From PV = nRT,
δ (PV) = PδV = δnRT, p (dV / dt) = (dn / dt) RT
And
Controlling P (dv / dt) to be a sine wave is equivalent to controlling the number of molecules fed into the sample chamber to be a sine wave. In general, since the number of gas molecules and pressure in a certain system are proportional (linear), nonlinearity can be corrected by this control method.

  Such control of the piezoelectric element 11 can be executed by calculation in the calculation unit 51. Based on the pressure detected by the pressure sensor 12, the calculation unit 51 performs a calculation according to the method (1) or (2), and the control unit 53 feedback-controls the piezoelectric element 11 according to the calculation result.

  As described above, according to the present embodiment, since the measurement is performed by the FR method after the sample chamber is configured by the microchannel, there is a problem in the case of configuring the sample chamber by the microchannel in the gas adsorption method. Can be resolved. In other words, the FR method allows measurement that is essentially unaffected by the amount of sample, so that even if the amount of catalyst in the channel is accurately controlled or cannot be measured accurately, high-precision measurement is possible. It becomes possible. Further, it is not necessary to keep the sample at the liquid nitrogen temperature, and measurement at an arbitrary temperature is possible. Furthermore, since any gas can be introduced, dynamic measurement with a gas of a type actually involved in the reaction, such as in the case of measurement with respect to a catalyst, is also possible.

  Further, as described above, by modulating the volume while correcting the nonlinearity of the pressure at the time of measurement, it is not necessary to consider the nonlinearity of the pressure, and the analysis becomes easy. Further, since the modulation width can be increased, a high S / N ratio can be obtained. Furthermore, since the modulation ratio with respect to the volume of the sample chamber can be made large, for example, the modulation width can be set to the same level as the volume, the volume of the sample chamber can be suppressed, and the apparatus can be downsized. Furthermore, there is no burden on the installation environment. Note that the method of modulating the volume while correcting the nonlinearity of the pressure during measurement according to the present invention is not limited by the configuration of the sample chamber. The present invention can be similarly applied to a case where the sample chamber is not constituted by a microchannel, and the present invention can be applied regardless of the volume of the sample chamber.

  Hereinafter, the measurement apparatus of Example 2 will be described with reference to FIG. This embodiment shows an example in which the measuring apparatus of the present invention is applied to a catalyst evaluation apparatus.

  FIG. 5 is a cross-sectional view showing the configuration of the measuring apparatus according to the second embodiment. The same components as those in the first embodiment are denoted by the same reference numerals, and the description thereof is omitted.

  As shown in FIG. 5, in the measurement apparatus of this embodiment, a semiconductor pressure sensor 21 for detecting the pressure in the sample chamber is attached to the microchannel device 2. In this case, since the pressure of the part in which the catalyst is accommodated can be detected, the pressure sensor 21 can be used for monitoring the pressure in the microchannel device 2 at the time of measurement.

  Similar to Example 1, according to this example, the sample chamber is configured with a microchannel and then the measurement is performed by the FR method, which eliminates the problem when the sample chamber is configured with a microchannel in the gas adsorption method. can do.

  Further, as described above, by modulating the volume while correcting the nonlinearity of the pressure at the time of measurement, it is not necessary to consider the nonlinearity of the pressure, and the analysis becomes easy. Further, since the modulation width can be increased, a high S / N ratio can be obtained. Furthermore, there is no burden on the installation environment.

  In the measuring apparatus and the measuring method according to the present invention, the measurement target is not limited. The measurement object is not limited to the catalyst, and for example, the size of the pores of the catalyst carrier, the adsorbent, the molecular sieve, the zeolite and the like can be measured. By measuring whether specific gas molecules enter the pores, or by measuring the diffusion rate in the pores, it is possible to obtain information for selecting the optimal catalyst carrier, adsorbent, molecular sieve, etc. it can. Furthermore, it can also be applied to the measurement of the tube diameter of carbon nanotubes.

  In addition, for example, an unknown gas can be analyzed by accommodating a sample whose pore size is known in advance, such as zeolite, in a sample chamber, and introducing and measuring the unknown gas.

  As described above, according to the measuring apparatus of the present invention, the analysis based on the response characteristic of the pressure measured by the pressure measuring unit with respect to the volume modulation by the volume modulating unit is performed. For this reason, when the sample chamber is configured using a microchannel, high-precision measurement is possible, and a wide range of measurements can be performed regardless of measurement conditions. Further, according to the measuring apparatus of the present invention, the volume can be modulated while correcting the nonlinearity of the pressure at the time of measurement. For this reason, it is not necessary to consider non-linearity in the pressure, and the analysis based on the response characteristic of the pressure becomes easy. Further, since the modulation width can be increased, a high S / N ratio can be obtained. Furthermore, according to the measurement method of the present invention, the volume can be modulated while correcting the nonlinearity of the pressure at the time of measurement. For this reason, it is not necessary to consider non-linearity in the pressure, and the analysis based on the response characteristic of the pressure becomes easy. Further, since the modulation width can be increased, a high S / N ratio can be obtained.

  The scope of application of the present invention is not limited to the above embodiment. The present invention can be widely applied to a measuring apparatus and a measuring method for measuring a sample in a sample chamber using the phenomenon of gas adsorption.

The block diagram which shows the measuring apparatus of this invention functionally. Sectional drawing which shows the structure of the measuring apparatus of Example 1. FIG. FIG. 2 is a block diagram illustrating a configuration of a control system in the measurement apparatus according to the first embodiment. 5 is a flowchart illustrating a processing procedure during measurement in the measurement apparatus according to the first embodiment. Sectional drawing which shows the structure of the measuring apparatus of Example 2. FIG.

Explanation of symbols

10 Microchannel 11 Piezoelectric element (volume modulation means, volume control means)
12 Semiconductor pressure sensor (pressure measuring means)
20 microchannel 51 calculation unit (analysis means, volume control means)
DESCRIPTION OF SYMBOLS 101 Sample chamber 102 Volume modulation means 103 Pressure measurement means 104 Analysis means 111 Volume modulation means 112 Pressure measurement means 113 Volume control means 114 Analysis means

Claims (13)

In a measuring device that measures the sample in the sample chamber using the phenomenon of gas adsorption,
The sample chamber is configured using a microchannel,
The measuring device is
Volume modulation means for modulating the volume of the sample chamber;
Pressure measuring means for measuring the pressure in the sample chamber;
Analysis means for performing an analysis based on a response characteristic of the pressure measured by the pressure measurement means with respect to modulation of the volume by the volume modulation means;
A measuring apparatus using gas adsorption, comprising: 2. The measuring apparatus using gas adsorption according to claim 1, wherein the analyzing means analyzes a pore distribution of the sample in the sample chamber. The sample chamber is configured by connecting a microchannel of a detachable microchannel device for storing a sample and a microchannel on the measurement apparatus side to which the volume modulation unit is attached. A measuring apparatus using gas adsorption according to 1 or 2. The measurement apparatus using gas adsorption according to claim 3, wherein the volume modulation means and the pressure measurement means are attached to a member on which a microchannel on the measurement apparatus side is formed. The measurement apparatus using gas adsorption according to claim 3, wherein the pressure measurement unit is incorporated in the microchannel device. The measuring apparatus using gas adsorption according to claim 1, wherein the volume modulation means is configured using a piezoelectric element that modulates the volume of the sample chamber. The said pressure measurement means is comprised using a semiconductor pressure sensor, The measuring apparatus using the gas adsorption | suction of any one of Claims 1-6 characterized by the above-mentioned. In the measuring device that measures the sample in the sample chamber based on the responsiveness of gas adsorption,
Volume modulation means for modulating the volume of the sample chamber;
Pressure measuring means for measuring the pressure in the sample chamber;
Volume control means for feedback controlling the volume modulation means based on the pressure measured by the pressure measurement means;
Analysis means for performing an analysis based on a response characteristic of the pressure measured by the pressure measurement means with respect to modulation of the volume by the volume modulation means;
A measuring apparatus using gas adsorption, comprising: 9. The measuring apparatus using gas adsorption according to claim 8, wherein the volume control means feedback-controls the volume modulation means so that the pressure measured by the pressure measurement means becomes a sine wave. The volume control means feedback-controls the volume modulation means so that a product of a pressure measured by the pressure measurement means and a value obtained by differentiating the volume with respect to time becomes a sine wave. 8. A measuring apparatus using gas adsorption according to 8. In a measurement method for measuring a sample in a sample chamber based on the gas adsorption response,
Modulating the volume of the sample chamber;
Measuring the pressure in the sample chamber;
Feedback controlling the modulation amount in the step of modulating the volume based on the pressure measured by the step of measuring the pressure;
Performing an analysis based on a response characteristic of the pressure measured by the step of measuring the pressure with respect to modulation of the volume by the step of modulating the volume;
A measurement method using gas adsorption, comprising: The feedback control of the modulation amount in the step of modulating the volume is performed so that the pressure measured in the step of measuring the pressure becomes a sine wave in the step of feedback controlling the modulation amount. A measurement method using gas adsorption described in 1. In the step of feedback controlling the modulation amount, the modulation amount in the step of modulating the volume so that the product of the pressure measured in the step of measuring the pressure and a value obtained by time differentiation of the volume becomes a sine wave. The measurement method using gas adsorption according to claim 11, wherein feedback control is performed.

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