- Email: [email protected]
Study of water vapor pressure equilibration in a vacuum system
Vacuum 98 (2013) 3e7
Contents lists available at SciVerse ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Study of water vapor pressure equilibration in a vacuum system b, * Makfir Sefa a, b, Janez Setina , Bojan Erjavec b a b
Lotric d.o.o, Selca, Slovenia Institute of Metals and Technology, SI-1000 Ljubljana, Slovenia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 July 2012 Received in revised form 15 November 2012 Accepted 19 November 2012
We have studied the approach to equilibrium pressure distribution after a sudden introduction of a given quantity of water vapor into a vacuum chamber. The time delay of a pressure reading of a spinning rotor gauge at the end of a 0.50 m and 0.935 m long stainless steel tube with inside diameter of 16 mm was measured. This time delay increased with decreasing pressure approximately as P0.55. With a 0.5 m tube the time delay was approximately 5 times shorter than with a 0.935 m tube. At 1 104 mbar the times to reach a 99.7% level of equilibrium at the end of 0.50 m and 0.935 m tubes were 60 s and 330 s, respectively. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Water vapor Adsorption Desorption Vacuum gauge calibration Spinning rotor gauge
1. Introduction We have studied the distribution of water vapor after a sudden introduction in conjunction with the development of a calibration technique of vacuum gauges for water vapor. For comparison calibration of vacuum gauges, the pressure inside the calibration chamber should be as uniform as possible. Calibration gas is admitted locally in the vacuum system and in the case of an adsorbing gas, like water vapor, the pressure distribution within the system can deviate significantly from the distribution of another non-adsorbing gas admitted at the same location. Water vapor adsorption and desorption on vacuum chamber walls play an important role during exposure to atmosphere and in the subsequent outgassing rate when the chamber is evacuated again. These phenomena have been studied by many authors. The number of adsorbed/desorbed monolayers can be determined by integration of desorbed flux and depend on the exposure time and relative humidity [1]. Another interesting method to determine surface coverage of water vapor by a radioactive tracer technique was also used to determine surface coverage [2,3]. The abovementioned studies show that several monolayers are adsorbed on technical surfaces during exposure to air moisture. Even exposure to relatively dry nitrogen flushing gas with only 0.02% moisture content leaves a considerable amount of adsorbed water [4]. Removal of adsorbed water is a slow process and the flux of
* Corresponding author. Tel.: þ386 1 4701 976; fax: þ386 1 4701 939. E-mail address: [email protected] (J. Setina). 0042-207X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.vacuum.2012.11.011
desorbed water molecules decreases with time of pumping as ta, a being in the range from 0.5 to 1.5 [5]. The long residence time of adsorbed water molecules on the surfaces presents a great challenge for the precise measurement of water vapor in vacuum systems [6]. The expected result of our study was to estimate the necessary waiting time to reach the same pressure (gas molecule density) at the location of the reference gauge and a gauge to be calibrated. To our knowledge no such study has been previously reported. We have used in our measurements spinning rotor gauges (SRG), because they are inert, operate at room temperature and have excellent linear response in the molecular regime. The SRG has also unsurpassable signal to noise level and short term stability compared to other inert vacuum gauges such as capacitance diaphragm gauges. The achievable signal to noise level of the SRG is of the order of 104 in the range of measured pressures from 104 mbar to 102 mbar and is therefore the only suitable high vacuum gauge for such measurements. 2. Experiment Our measurement system is shown in Fig. 1. It is essentially a static expansion calibration system with a large chamber CH1 ¼ 10 l and a small chamber CH2 ¼ 0.04 l. Both chambers are made of austenitic stainless steel 304L. Inner surfaces have a standard finish of commercial Conflat type fittings. All joints are made with Conflat flanges and Cu gaskets and all valves are bakeable “all-metal” type. Pumps are turbomolecular backed with membrane fore-pumps.
4
M. Sefa et al. / Vacuum 98 (2013) 3e7
0.935 m
Setup3 0.50 m
Setup2
Setup1
SRG1
CCG
SRG2
CH1
CDG2
V2
V5
V3 CH2
CDG1
V4
V1 H2O TMP
TMP
Fig. 1. Measurement system for studies of time delay of water vapor. SRG1, SRG2 e spinning rotor gauges; CDG1 e capacitance diaphragm gauge 10 Pa FS, CDG2 e capacitance diaphragm gauge 10 kPa FS; CCG e cold cathode ionization gauge; V1, V2, V3, V4, V5 e all metal vacuum valves; CH1, CH2 e vacuum chambers; TMP e turbomolecular pumps.
The water-vapor source is made of stainless steel reservoir filled partly with degassed liquid water. To stabilize reservoir temperature we put it in a water bath which is in an insulating Dewar. We keep reservoir temperature below ambient temperature to avoid condensation of water vapor in the vacuum chambers. Partial pressure of water vapor in the reservoir can be regulated in a range from 6.1 mbar to approximately 23 mbar by varying the temperature of the water bath from 0 C to 20 C. We attached to the CH1 a CF 16 T-piece and connected two Spinning Rotor Gauges to it. We made following variations of this connection: Setup 1: SRG1 and SRG 2 were both connected directly to the Tpiece Setup 2: We inserted a 0.50 m long CF16 tube between the T piece and SRG2 Setup 3: We inserted a 0.935 m long CF16 tube between the T piece and SRG2 Experiments with water vapor were done in following way. CH1 was pumped by the TMP1 for several hours to reach a pressure below 1 107 mbar, measured by the cold cathode vacuum gauge (CCG). CH2 was evacuated separately by TMP2 (valve V2 between chambers was closed). Then valve V5 was closed and the desired amount of water vapor was carefully dosed from the water reservoir through valve V4. Water vapor pressure in CH2 was measured with CDG2. We waited for 10 min until the pressure in CH2 stabilized. Then the valves V1 and V3 were closed and V2 opened, to expand water vapor into the previously evacuated CH1. The initial pressure of water vapor in CH2 before expansion was in the range from 0.1 mbar to 1 mbar. Both SRGs and CDG1 (which was also connected to CH1) were connected to a personal computer so that measured values were continuously acquired and stored by a LabView program. Shortly before expansion the two SRG rotors were re-accelerated to the upper rotational frequency and “synchronized” by issuing a command to both units to restart measurement cycles practically
at the same time. In our experiments we used a frequency window from 785 Hz to 805 Hz and sampling interval of 10 s. After this synchronization and before water vapor expansion the residual drag of each SRG was determined. In all measurements we took into account also the frequency dependence of residual drag. CDG1 which has a much faster response time than the SRG was used to determine the starting time t ¼ 0 for the time scale after expansion. After water vapor expansion into CH1 the measured pressures of SRG1 and SRG2 were compared. In setup 1, where both SRGs were mounted symmetrically (having the same distance from CH1), the measured pressures were the same while, in setup 2 and 3, we observed a delay of readings of SRG2 compared to SRG1. This delay of SRG2, which was mounted at the end of 0.50 m or 0.935 m tubes, was due to adsorption of water vapor inside the tube. There is a slight difference in momentum accommodation coefficients s of both SRG rotors, but one can expect that values are close to 1. In our measurements the absolute values of s are not so important, but their ratio is very important. Measurements were done with value s ¼ 1 entered into SRG controllers. The ratio of momentum accommodation coefficients was then determined for each measurement cycle from measured readings RSRG1 and RSRG2 which were taken two hours or more after expansion. At this time the relative difference of local pressure of water vapor at the location of SRGs was much less than 0.1%. The ratio of readings is related to the relative ratio of momentum accommodation coefficients as:
srel ¼ sSRG2 =sSRG1 ¼ RSRG2 =RSRG1
(1)
SRG readings RSRG are displayed values with a correction for residual drag including its frequency dependence, but with the value s ¼ 1 entered into the SRG controllers. In our data evaluations we have assumed that the momentum accommodation coefficient of SRG1 is exactly sSRG1 ¼ 1 (so PSRG1 ¼ RSRG1) and the momentum accommodation coefficient of SRG2 is sSRG2 ¼ srel, therefore PSRG2 ¼ RSRG2/srel. We can define a deviation from equilibrium D as:
D ¼ 1 PSRG2 =PSRG1
(2)
When equilibrium is reached, we get PSRG2/PSRG1 ¼ 1 and D ¼ 0.
3. Results First we have checked the data acquisition system and response of both SRGs to a sudden increase of water vapor pressure in Setup 1. The ratio of SRG pressures is shown in Fig. 2. An example of measured pressures in Setup 3 after expansion of water vapor from CH2 at 0.4 mbar is shown in Fig. 3. The time of measurement was extended up to 25 h after expansion. In this figure the pressures of SRG1 and SRG2 look essentially the same and, only when we calculate the ratio of both pressures, the small difference in the first hour becomes evident (Fig. 4). The calculated ratio PSRG2/PSRG1 of each measurement run was modeled with neural networks, as shown in Fig. 5. The modeled ratio was used to calculate the time delay to reach different values of deviation from equilibrium D (3%, 1%, 0.3%, and 0.1%). With modeling we eliminated noise in the calculated pressure ratio. This enables us to estimate more accurately the time delay at lower pressures; especially for D ¼ 0.3% and D ¼ 0.1%. We have repeated measurements in Setup 2 and Setup 3 to get several data points in the range of expanded pressure from 4 105 mbar to 2 103 mbar. A summary of all results is given in next section.
1.002
1.002
1.000
1.000 P_SRG2 / P_SRG1
P_SRG2 / P_SRG1
M. Sefa et al. / Vacuum 98 (2013) 3e7
0.998 0.996 0.994
0.996 0.994 0.992
0.990
0.990 100
200
300
400
500
1.002 1.000 0.998 0.996 0.994 0.992 0.990 0
0.998
0.992
0
5
5
10 15 Time / h
Time / s Fig. 2. Ratio PSRG2/PSRG1 measured in Setup 1. Pressure after expansion was 5.9 105 mbar.
4. Discussion In the case of Setup 1 the measured pressures of both SRGs are essentially the same, so that we get a ratio PSRG2/PSRG1 ¼ 1 practically immediately after expansion of water vapor (Fig. 2). It will be discussed below that, after expansion, the water vapor is absorbed on surfaces of CH1 for an extended period of time so the pressure is continually changing and significant change of pressure can happen during one integration period (10 s in our case). For these measurements it is therefore very important that both SRGs are “synchronized” so that the “integration cycles” of corresponding readings start simultaneously in both SRGs. Only in this case the two related SRG pressures are obtained as the mean value during integration intervals that appear at the same time. In all measurements we have observed adsorption of a considerable amount of water molecules on the surfaces of the chamber V2. The typical example of pressure curve after expansion is shown in Fig. 3. After fast decrease of water partial pressure in the first few minutes, the adsorption continued at a significantly reduced rate, but for a very long time. Even after 10 h the water pressure was continuously decreasing, but at very slow rate (Fig. 3). The initial pressure for this measurement run was 0.68 mbar. According to the volume ratio of CH1 and CH2, which was measured with nitrogen and is 251, the pressure without adsorption should be
600
900
1200
Time / s
0
600
300
20
25
Fig. 4. Ratio PSRG2/PSRG1 for measurements from Fig. 3. Inset shows the ratio within first 20 min after expansion.
2.7 103 mbar. The pressure 10 h after expansion was 3.5 104 mbar. This means that only approximately 13% of initial water vapor was in the gas phase and the rest (0.025 mbar l) was adsorbed on the surface. The area of CH1 is approximately 6500 cm2. Taking the monolayer coverage of water vapor on a flat surface as 1 1015 molecules/cm2, this means there is 0.10 of a monolayer coverage on the surfaces of CH1. In Setup 2 and 3 there is longer travel time of gas molecules from the chamber to the position of SRG2 compared to the position of SRG1. This results in some time delay also for non-adsorbing gas. We have estimated that, for the range of pressures in our experiment, this time delay is less than 10 s. It was checked with nitrogen and the measured ratio SRG2/SRG1 was also in the case of Setup 2 and 3 essentially the same as in Fig. 2. This means that the longer travel time of molecules to the position of SRG2 has negligible contribution to the time delay compared to the delay caused by adsorption on the surfaces. With Setup 2 and 3, the measured pressure of SRG2 after expansion of water vapor is smaller than the pressure of SRG1 for a considerably longer time as in the case of a non-adsorbing gas. For values of calculated ratio PSRG2/PSRG1 >0.99 the noise becomes significant. We applied neural network modeling for approximation of the noisy data with a smooth curve, as shown in Fig. 5. We have used an extension for MS Excel NEURALIST (Cheshire Ltd.).
1.002
0.0014 P_SRG2 / P_SRG1
1.000
P_SRG / mbar
0.0012 0.0010 0.0008 0.0006 0.0004
0.998 0.996 0.994 0.992
0.0002 0.990
0.0000 0
5
10 15 Time / h SRG1
20
25
SRG2
Fig. 3. Example of time dependence of pressure measured with SRG1 and SRG2 after expansion of water vapor from V1 into V2. Measurements were done in Setup 3.
0
500
1000
1500
2000
Time / s Measurement
Modeling_NN
Fig. 5. Neural network modeling of measured ratio PSRG2/PSRG1. Setup 3, pressure was 3.8 105 mbar.
6
M. Sefa et al. / Vacuum 98 (2013) 3e7
104
10
3
102
10
1
10
0
10
-5
10-4
10
-3
10
-2
Fig. 6. Calculated time delays for given D as a function of water vapor pressure in Setup 2.
This is a very useful tool for general nonlinear modeling. The modeled curve is certainly more convenient to determine the time delay to reach a certain deviation from equilibrium D, which was defined by Eq. (2). Results of measured time delay s for Setup 2 are presented in Fig. 6 and for Setup 3 in Fig. 7. On a log (s) versus log (P) graph the time delays for given D appear to be on a straight line. The lines for different D have nearly the same slope and are only shifted in the vertical direction. Comparison of time delay for D ¼ 0.3% measured in Setup 2 and Setup 3 is presented in Fig. 8. The data points for Setup 2 can be approximated with
s¼
0:37 P 0:55
(3)
and for setup 3 with:
s¼
1:85 P 0:56
(4)
These approximations are shown as straight lines in Fig. 8.
Fig. 7. Calculated time delays for given D as a function of water vapor pressure in Setup 3.
Fig. 8. Comparison of calculated time delays for D ¼ 0.3% in Setup 2 and Setup 3 as a function of water vapor pressure. Symbols: measured data, lines: fits of measured data according to Eqs. (3) and (4).
It is somehow surprising that the time delay in Setup 3 is around 5 times longer than in Setup 2. The ratio of lengths is approximately 1.9. One would expect that the time delay would scale roughly with the surface of the intermediate tube, and ratio of surfaces is equal to the ratio of lengths. This was also a quite surprising result for us and we have made careful analysis of possible errors in measurements. We have repeated the whole set of measurement in Setup 2 and 3 and we obtained repeatable results. At this stage we cannot give an explanation for the 5 times longer time delay in the 2 times longer intermediate tube in our experiment, without making much more measurements with tubes of other lengths and diameters. 5. Conclusions We have made a study of the time delay to reach a uniform pressure distribution inside a vacuum chamber after introduction of water vapor. Measurements were done in a static mode. This means that the system was isolated from the pumps and then different quantities of water vapor were introduced. We have observed adsorption of a considerable amount of water molecules on the surfaces of the chamber. After fast decrease of water partial pressure in the first 10e15 min, the adsorption continued at a significantly reduced rate, but for a very long time. Two SRGs were connected to the chamber through connection tubes of different lengths which enabled precise measurements of time delays in the pressure range from 4 105 mbar to 2 103 mbar. At pressure 1 104 mbar the time delay to reach deviation from equilibrium D ¼ 0.3% was around 60 s in the case of an extension tube with length 0.50 m (Setup 2). In the case of an extension tube with nearly double length of 0.935 m (Setup 3) the time delay was 330 s, which is a 5.5 times longer time. The inner diameter of the extension tubes was 16 mm in both cases. The time delay varied with pressure as P0.55. In the time interval less than 1000 s after expansion the pressure in the system was still decreasing quite fast, which means that a nearly uniform distribution of water vapor inside the extension tube and in the whole system was achieved much faster than equilibrium surface coverage. Results of the presented study are important for estimation of the necessary waiting time for comparison calibration of vacuum gauges with water vapor.
M. Sefa et al. / Vacuum 98 (2013) 3e7
Acknowledgment
References
One of the authors (M. Sefa) acknowledges a partial financial support by the European Union, European Social Fund. Operation was implemented in the framework of the Operational Programme for Human Resources Development for the Period 2007e2013.
[1] [2] [3] [4] [5] [6]
Li Minxu, Dylla HF. JVST A 1994;12:1772. Dobrozemsky R. JVST A 1987;5:2520. Dobrozemsky R, Menhart S, Buchtela K. JVST A 2007;25:551. Siefering KL, Whitlock WH. JVST A 1994;12:2685. Li Minxu, Dylla HF. JVST A 1993;11:1702. Basford JA. JVST A 1994;12:1778.
7
Contents lists available at SciVerse ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Study of water vapor pressure equilibration in a vacuum system b, * Makfir Sefa a, b, Janez Setina , Bojan Erjavec b a b
Lotric d.o.o, Selca, Slovenia Institute of Metals and Technology, SI-1000 Ljubljana, Slovenia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 July 2012 Received in revised form 15 November 2012 Accepted 19 November 2012
We have studied the approach to equilibrium pressure distribution after a sudden introduction of a given quantity of water vapor into a vacuum chamber. The time delay of a pressure reading of a spinning rotor gauge at the end of a 0.50 m and 0.935 m long stainless steel tube with inside diameter of 16 mm was measured. This time delay increased with decreasing pressure approximately as P0.55. With a 0.5 m tube the time delay was approximately 5 times shorter than with a 0.935 m tube. At 1 104 mbar the times to reach a 99.7% level of equilibrium at the end of 0.50 m and 0.935 m tubes were 60 s and 330 s, respectively. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Water vapor Adsorption Desorption Vacuum gauge calibration Spinning rotor gauge
1. Introduction We have studied the distribution of water vapor after a sudden introduction in conjunction with the development of a calibration technique of vacuum gauges for water vapor. For comparison calibration of vacuum gauges, the pressure inside the calibration chamber should be as uniform as possible. Calibration gas is admitted locally in the vacuum system and in the case of an adsorbing gas, like water vapor, the pressure distribution within the system can deviate significantly from the distribution of another non-adsorbing gas admitted at the same location. Water vapor adsorption and desorption on vacuum chamber walls play an important role during exposure to atmosphere and in the subsequent outgassing rate when the chamber is evacuated again. These phenomena have been studied by many authors. The number of adsorbed/desorbed monolayers can be determined by integration of desorbed flux and depend on the exposure time and relative humidity [1]. Another interesting method to determine surface coverage of water vapor by a radioactive tracer technique was also used to determine surface coverage [2,3]. The abovementioned studies show that several monolayers are adsorbed on technical surfaces during exposure to air moisture. Even exposure to relatively dry nitrogen flushing gas with only 0.02% moisture content leaves a considerable amount of adsorbed water [4]. Removal of adsorbed water is a slow process and the flux of
* Corresponding author. Tel.: þ386 1 4701 976; fax: þ386 1 4701 939. E-mail address: [email protected] (J. Setina). 0042-207X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.vacuum.2012.11.011
desorbed water molecules decreases with time of pumping as ta, a being in the range from 0.5 to 1.5 [5]. The long residence time of adsorbed water molecules on the surfaces presents a great challenge for the precise measurement of water vapor in vacuum systems [6]. The expected result of our study was to estimate the necessary waiting time to reach the same pressure (gas molecule density) at the location of the reference gauge and a gauge to be calibrated. To our knowledge no such study has been previously reported. We have used in our measurements spinning rotor gauges (SRG), because they are inert, operate at room temperature and have excellent linear response in the molecular regime. The SRG has also unsurpassable signal to noise level and short term stability compared to other inert vacuum gauges such as capacitance diaphragm gauges. The achievable signal to noise level of the SRG is of the order of 104 in the range of measured pressures from 104 mbar to 102 mbar and is therefore the only suitable high vacuum gauge for such measurements. 2. Experiment Our measurement system is shown in Fig. 1. It is essentially a static expansion calibration system with a large chamber CH1 ¼ 10 l and a small chamber CH2 ¼ 0.04 l. Both chambers are made of austenitic stainless steel 304L. Inner surfaces have a standard finish of commercial Conflat type fittings. All joints are made with Conflat flanges and Cu gaskets and all valves are bakeable “all-metal” type. Pumps are turbomolecular backed with membrane fore-pumps.
4
M. Sefa et al. / Vacuum 98 (2013) 3e7
0.935 m
Setup3 0.50 m
Setup2
Setup1
SRG1
CCG
SRG2
CH1
CDG2
V2
V5
V3 CH2
CDG1
V4
V1 H2O TMP
TMP
Fig. 1. Measurement system for studies of time delay of water vapor. SRG1, SRG2 e spinning rotor gauges; CDG1 e capacitance diaphragm gauge 10 Pa FS, CDG2 e capacitance diaphragm gauge 10 kPa FS; CCG e cold cathode ionization gauge; V1, V2, V3, V4, V5 e all metal vacuum valves; CH1, CH2 e vacuum chambers; TMP e turbomolecular pumps.
The water-vapor source is made of stainless steel reservoir filled partly with degassed liquid water. To stabilize reservoir temperature we put it in a water bath which is in an insulating Dewar. We keep reservoir temperature below ambient temperature to avoid condensation of water vapor in the vacuum chambers. Partial pressure of water vapor in the reservoir can be regulated in a range from 6.1 mbar to approximately 23 mbar by varying the temperature of the water bath from 0 C to 20 C. We attached to the CH1 a CF 16 T-piece and connected two Spinning Rotor Gauges to it. We made following variations of this connection: Setup 1: SRG1 and SRG 2 were both connected directly to the Tpiece Setup 2: We inserted a 0.50 m long CF16 tube between the T piece and SRG2 Setup 3: We inserted a 0.935 m long CF16 tube between the T piece and SRG2 Experiments with water vapor were done in following way. CH1 was pumped by the TMP1 for several hours to reach a pressure below 1 107 mbar, measured by the cold cathode vacuum gauge (CCG). CH2 was evacuated separately by TMP2 (valve V2 between chambers was closed). Then valve V5 was closed and the desired amount of water vapor was carefully dosed from the water reservoir through valve V4. Water vapor pressure in CH2 was measured with CDG2. We waited for 10 min until the pressure in CH2 stabilized. Then the valves V1 and V3 were closed and V2 opened, to expand water vapor into the previously evacuated CH1. The initial pressure of water vapor in CH2 before expansion was in the range from 0.1 mbar to 1 mbar. Both SRGs and CDG1 (which was also connected to CH1) were connected to a personal computer so that measured values were continuously acquired and stored by a LabView program. Shortly before expansion the two SRG rotors were re-accelerated to the upper rotational frequency and “synchronized” by issuing a command to both units to restart measurement cycles practically
at the same time. In our experiments we used a frequency window from 785 Hz to 805 Hz and sampling interval of 10 s. After this synchronization and before water vapor expansion the residual drag of each SRG was determined. In all measurements we took into account also the frequency dependence of residual drag. CDG1 which has a much faster response time than the SRG was used to determine the starting time t ¼ 0 for the time scale after expansion. After water vapor expansion into CH1 the measured pressures of SRG1 and SRG2 were compared. In setup 1, where both SRGs were mounted symmetrically (having the same distance from CH1), the measured pressures were the same while, in setup 2 and 3, we observed a delay of readings of SRG2 compared to SRG1. This delay of SRG2, which was mounted at the end of 0.50 m or 0.935 m tubes, was due to adsorption of water vapor inside the tube. There is a slight difference in momentum accommodation coefficients s of both SRG rotors, but one can expect that values are close to 1. In our measurements the absolute values of s are not so important, but their ratio is very important. Measurements were done with value s ¼ 1 entered into SRG controllers. The ratio of momentum accommodation coefficients was then determined for each measurement cycle from measured readings RSRG1 and RSRG2 which were taken two hours or more after expansion. At this time the relative difference of local pressure of water vapor at the location of SRGs was much less than 0.1%. The ratio of readings is related to the relative ratio of momentum accommodation coefficients as:
srel ¼ sSRG2 =sSRG1 ¼ RSRG2 =RSRG1
(1)
SRG readings RSRG are displayed values with a correction for residual drag including its frequency dependence, but with the value s ¼ 1 entered into the SRG controllers. In our data evaluations we have assumed that the momentum accommodation coefficient of SRG1 is exactly sSRG1 ¼ 1 (so PSRG1 ¼ RSRG1) and the momentum accommodation coefficient of SRG2 is sSRG2 ¼ srel, therefore PSRG2 ¼ RSRG2/srel. We can define a deviation from equilibrium D as:
D ¼ 1 PSRG2 =PSRG1
(2)
When equilibrium is reached, we get PSRG2/PSRG1 ¼ 1 and D ¼ 0.
3. Results First we have checked the data acquisition system and response of both SRGs to a sudden increase of water vapor pressure in Setup 1. The ratio of SRG pressures is shown in Fig. 2. An example of measured pressures in Setup 3 after expansion of water vapor from CH2 at 0.4 mbar is shown in Fig. 3. The time of measurement was extended up to 25 h after expansion. In this figure the pressures of SRG1 and SRG2 look essentially the same and, only when we calculate the ratio of both pressures, the small difference in the first hour becomes evident (Fig. 4). The calculated ratio PSRG2/PSRG1 of each measurement run was modeled with neural networks, as shown in Fig. 5. The modeled ratio was used to calculate the time delay to reach different values of deviation from equilibrium D (3%, 1%, 0.3%, and 0.1%). With modeling we eliminated noise in the calculated pressure ratio. This enables us to estimate more accurately the time delay at lower pressures; especially for D ¼ 0.3% and D ¼ 0.1%. We have repeated measurements in Setup 2 and Setup 3 to get several data points in the range of expanded pressure from 4 105 mbar to 2 103 mbar. A summary of all results is given in next section.
1.002
1.002
1.000
1.000 P_SRG2 / P_SRG1
P_SRG2 / P_SRG1
M. Sefa et al. / Vacuum 98 (2013) 3e7
0.998 0.996 0.994
0.996 0.994 0.992
0.990
0.990 100
200
300
400
500
1.002 1.000 0.998 0.996 0.994 0.992 0.990 0
0.998
0.992
0
5
5
10 15 Time / h
Time / s Fig. 2. Ratio PSRG2/PSRG1 measured in Setup 1. Pressure after expansion was 5.9 105 mbar.
4. Discussion In the case of Setup 1 the measured pressures of both SRGs are essentially the same, so that we get a ratio PSRG2/PSRG1 ¼ 1 practically immediately after expansion of water vapor (Fig. 2). It will be discussed below that, after expansion, the water vapor is absorbed on surfaces of CH1 for an extended period of time so the pressure is continually changing and significant change of pressure can happen during one integration period (10 s in our case). For these measurements it is therefore very important that both SRGs are “synchronized” so that the “integration cycles” of corresponding readings start simultaneously in both SRGs. Only in this case the two related SRG pressures are obtained as the mean value during integration intervals that appear at the same time. In all measurements we have observed adsorption of a considerable amount of water molecules on the surfaces of the chamber V2. The typical example of pressure curve after expansion is shown in Fig. 3. After fast decrease of water partial pressure in the first few minutes, the adsorption continued at a significantly reduced rate, but for a very long time. Even after 10 h the water pressure was continuously decreasing, but at very slow rate (Fig. 3). The initial pressure for this measurement run was 0.68 mbar. According to the volume ratio of CH1 and CH2, which was measured with nitrogen and is 251, the pressure without adsorption should be
600
900
1200
Time / s
0
600
300
20
25
Fig. 4. Ratio PSRG2/PSRG1 for measurements from Fig. 3. Inset shows the ratio within first 20 min after expansion.
2.7 103 mbar. The pressure 10 h after expansion was 3.5 104 mbar. This means that only approximately 13% of initial water vapor was in the gas phase and the rest (0.025 mbar l) was adsorbed on the surface. The area of CH1 is approximately 6500 cm2. Taking the monolayer coverage of water vapor on a flat surface as 1 1015 molecules/cm2, this means there is 0.10 of a monolayer coverage on the surfaces of CH1. In Setup 2 and 3 there is longer travel time of gas molecules from the chamber to the position of SRG2 compared to the position of SRG1. This results in some time delay also for non-adsorbing gas. We have estimated that, for the range of pressures in our experiment, this time delay is less than 10 s. It was checked with nitrogen and the measured ratio SRG2/SRG1 was also in the case of Setup 2 and 3 essentially the same as in Fig. 2. This means that the longer travel time of molecules to the position of SRG2 has negligible contribution to the time delay compared to the delay caused by adsorption on the surfaces. With Setup 2 and 3, the measured pressure of SRG2 after expansion of water vapor is smaller than the pressure of SRG1 for a considerably longer time as in the case of a non-adsorbing gas. For values of calculated ratio PSRG2/PSRG1 >0.99 the noise becomes significant. We applied neural network modeling for approximation of the noisy data with a smooth curve, as shown in Fig. 5. We have used an extension for MS Excel NEURALIST (Cheshire Ltd.).
1.002
0.0014 P_SRG2 / P_SRG1
1.000
P_SRG / mbar
0.0012 0.0010 0.0008 0.0006 0.0004
0.998 0.996 0.994 0.992
0.0002 0.990
0.0000 0
5
10 15 Time / h SRG1
20
25
SRG2
Fig. 3. Example of time dependence of pressure measured with SRG1 and SRG2 after expansion of water vapor from V1 into V2. Measurements were done in Setup 3.
0
500
1000
1500
2000
Time / s Measurement
Modeling_NN
Fig. 5. Neural network modeling of measured ratio PSRG2/PSRG1. Setup 3, pressure was 3.8 105 mbar.
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M. Sefa et al. / Vacuum 98 (2013) 3e7
104
10
3
102
10
1
10
0
10
-5
10-4
10
-3
10
-2
Fig. 6. Calculated time delays for given D as a function of water vapor pressure in Setup 2.
This is a very useful tool for general nonlinear modeling. The modeled curve is certainly more convenient to determine the time delay to reach a certain deviation from equilibrium D, which was defined by Eq. (2). Results of measured time delay s for Setup 2 are presented in Fig. 6 and for Setup 3 in Fig. 7. On a log (s) versus log (P) graph the time delays for given D appear to be on a straight line. The lines for different D have nearly the same slope and are only shifted in the vertical direction. Comparison of time delay for D ¼ 0.3% measured in Setup 2 and Setup 3 is presented in Fig. 8. The data points for Setup 2 can be approximated with
s¼
0:37 P 0:55
(3)
and for setup 3 with:
s¼
1:85 P 0:56
(4)
These approximations are shown as straight lines in Fig. 8.
Fig. 7. Calculated time delays for given D as a function of water vapor pressure in Setup 3.
Fig. 8. Comparison of calculated time delays for D ¼ 0.3% in Setup 2 and Setup 3 as a function of water vapor pressure. Symbols: measured data, lines: fits of measured data according to Eqs. (3) and (4).
It is somehow surprising that the time delay in Setup 3 is around 5 times longer than in Setup 2. The ratio of lengths is approximately 1.9. One would expect that the time delay would scale roughly with the surface of the intermediate tube, and ratio of surfaces is equal to the ratio of lengths. This was also a quite surprising result for us and we have made careful analysis of possible errors in measurements. We have repeated the whole set of measurement in Setup 2 and 3 and we obtained repeatable results. At this stage we cannot give an explanation for the 5 times longer time delay in the 2 times longer intermediate tube in our experiment, without making much more measurements with tubes of other lengths and diameters. 5. Conclusions We have made a study of the time delay to reach a uniform pressure distribution inside a vacuum chamber after introduction of water vapor. Measurements were done in a static mode. This means that the system was isolated from the pumps and then different quantities of water vapor were introduced. We have observed adsorption of a considerable amount of water molecules on the surfaces of the chamber. After fast decrease of water partial pressure in the first 10e15 min, the adsorption continued at a significantly reduced rate, but for a very long time. Two SRGs were connected to the chamber through connection tubes of different lengths which enabled precise measurements of time delays in the pressure range from 4 105 mbar to 2 103 mbar. At pressure 1 104 mbar the time delay to reach deviation from equilibrium D ¼ 0.3% was around 60 s in the case of an extension tube with length 0.50 m (Setup 2). In the case of an extension tube with nearly double length of 0.935 m (Setup 3) the time delay was 330 s, which is a 5.5 times longer time. The inner diameter of the extension tubes was 16 mm in both cases. The time delay varied with pressure as P0.55. In the time interval less than 1000 s after expansion the pressure in the system was still decreasing quite fast, which means that a nearly uniform distribution of water vapor inside the extension tube and in the whole system was achieved much faster than equilibrium surface coverage. Results of the presented study are important for estimation of the necessary waiting time for comparison calibration of vacuum gauges with water vapor.
M. Sefa et al. / Vacuum 98 (2013) 3e7
Acknowledgment
References
One of the authors (M. Sefa) acknowledges a partial financial support by the European Union, European Social Fund. Operation was implemented in the framework of the Operational Programme for Human Resources Development for the Period 2007e2013.
[1] [2] [3] [4] [5] [6]
Li Minxu, Dylla HF. JVST A 1994;12:1772. Dobrozemsky R. JVST A 1987;5:2520. Dobrozemsky R, Menhart S, Buchtela K. JVST A 2007;25:551. Siefering KL, Whitlock WH. JVST A 1994;12:2685. Li Minxu, Dylla HF. JVST A 1993;11:1702. Basford JA. JVST A 1994;12:1778.
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