Uncertainty Evaluation of the New Setup for Measurement of Water-Vapor Permeation Rate by a Dew-Point Sensor

Transcription

1 Int J Thermophys (2012) 33: DOI /s Uncertainty Evaluation of the New Setup for Measurement of Water-Vapor Permeation Rate by a Dew-Point Sensor D. Hudoklin J. Šetina J. Drnovšek Received: 31 March 2010 / Accepted: 11 May 2012 / Published online: 4 June 2012 Springer Science+Business Media, LLC 2012 Abstract The measurement of the water-vapor permeation rate (WVPR) through materials is very important in many industrial applications such as the development of new fabrics and construction materials, in the semiconductor industry, packaging, vacuum techniques, etc. The demand for this kind of measurement grows considerably and thus many different methods for measuring the WVPR are developed and standardized within numerous national and international standards. However, comparison of existing methods shows a low level of mutual agreement. The objective of this paper is to demonstrate the necessary uncertainty evaluation for WVPR measurements, so as to provide a basis for development of a corresponding reference measurement standard. This paper presents a specially developed measurement setup, which employs a precision dew-point sensor for WVPR measurements on specimens of different shapes. The paper also presents a physical model, which tries to account for both dynamic and quasi-static methods, the common types of WVPR measurements referred to in standards and scientific publications. An uncertainty evaluation carried out according to the ISO/IEC guide to the expression of uncertainty in measurement (GUM) shows the relative expanded (k = 2) uncertainty to be 3.0 % for WVPR of 6.71 mg h 1 (corresponding to permeance of 30.4 mg m 2 day 1 hpa 1 ). Keywords Dew point Humidity measurements Permeance Permeation Uncertainty Water-vapor permeation rate Water-vapor transmission rate D. Hudoklin (B) J. Drnovšek Metrology Institute of the Republic of Slovenia, University of Ljubljana, Faculty of Electrical Engineering, Laboratory of Metrology and Quality (MIRS/UL-FE/LMK), Ljubljana, Slovenia domen.hudoklin@fe.uni-lj.si J. Šestina Institute of Metals and Technology (MIRS/IMT-LMT), Ljubljana, Slovenia

2 1596 Int J Thermophys (2012) 33: Introduction Measurement of the water-vapor permeation rate (WVPR) through materials has a very important role in many applications, such as measurement of the vapor barrier quality in packaging of food and in drugs; measurement of fabrics breathability in the textile industry [1,2]; determination of moisture management and durability of construction materials [3 7]; in vacuum techniques; in the semiconductor industry as a reference for trace moisture measurements [8], etc. Water-vapor permeation measurement is also a subject of considerable scientific interest [1 8]. For these reasons, many national and international standards, such as ISO15106 series [9], ISO21129 [10], ISO12572 [11], ASTM E96/E96M-05 [12], etc., deal with this topic. According to these standards, water-vapor permeation is expressed by several similar parameters, such as the WVTR, permeance, and permeability. Methods for WVPR measurement as reported above are commonly grouped in either so-called quasi-static or dynamic methods (see Sect. 3). For both methods the permeation rate is determined using hygrometry (measurement of humidity), which allows traceability to well-established standards. The main motivation for the study presented in the paper is to develop a measurement setup, which requires metrological characterization with an uncertainty evaluation according to the ISO/IEC guide to the expression of uncertainty in measurement (GUM) [13]. Standards and publications listed above only indirectly address the uncertainty evaluation, by referring to [3], in which uncertainty components for the quasi-static method are discussed. For dynamic methods, some recent research presented in [8] shows evaluation of uncertainty for a WVPR measurement setup, which is used for specific applications in the semi-conductor industry for very low permeation rates. The study was carried out in our national laboratory MIRS/UL-FE/LMK, which is a holder of the Slovenian national temperature and humidity standards. 2 Measurement Setup The measurement setup presented in this paper uses a dynamic method for WVPR measurement. It is similar to systems used for vapor leak tests [14]; however, different in physical background. Figure 1 shows a schematic diagram of the measurement setup. The wet side of the specimen is controlled by a humidity generator (Thunder Scientific Model 2500), which provides a stable temperature in the range from 10 Cto+70 C and a relative humidity from 10 %rh to 95 %rh. The dry side of the specimen is purged by dry nitrogen carrier gas using a mass flow controller (MFC), which also measures the output volumetric flow. The gas flow of the setup can be set to a minimum of 0.1 L min 1. A pressure sensor measures the absolute pressure of the carrier gas at the MFC output. A secondary barometer is used to measure the barometric pressure. The carrier gas accumulates moisture permeating through the specimen from the wet side and is then passed through a precision dew-point sensor MBW 373H, which monitors its dew point. The same sensor is alternately used to measure the humidity of the wet side by manipulating valves 1 and 2 and by turning on the downstream pump to compensate for the MFC. In a different setup, the

3 Int J Thermophys (2012) 33: temperature and relative humidity controlled chamber dry N 2 MFC pressure meter, P c wet side dry side sample cell sample material 1 2 precision dew-point sensor pressure meter, P s pump Fig. 1 Schematic diagram of the setup for WVPR measurement humidity of the wet side can be measured in parallel with a secondary dew-point sensor. The measurement setup allows measurement of permeation through flat or tubeshaped sample material of different shapes used in various applications. Tube-shaped specimens can be coupled to stainless-steel tubes with Swagelok couplings, using special tube inserts to insure a tight connection. Depending on the expected permeation rate and consequently the lowest water-vapor concentration in the exhausted gas, specimens are prepared in different sizes. If the sample is more than 0.4 m long, it is put in the chamber of the humidity generator and coupled to the stainless-steel tube coming from the MFC. On the other end it is coupled to the stainless-steel tube going to the dew-point sensor. The wet side in this case is the entire chamber. Shorter specimens are inserted in a specially designed cell (see Fig. 2a) to insure more uniform humidity and temperature distributions. The cell is again placed in the humidity generator s chamber so that the temperature at which permeation is to be measured is stable and well defined measured by calibrated platinum resistance thermometer. A constant flow of generated humid gas (air) is fed through the wet side of the cell. The (a) humid gas metal gasket exhaust carrier (dry) gas to sensor fitting sample material (b) carrier (dry) gas to sensor leak test port sample material exhaust humid gas Fig. 2 Cell for measurement of water-vapor permeation through (a) tube-shaped or (b) flat specimens

4 1598 Int J Thermophys (2012) 33: design allows the cell to be extended by adding extensions with 25.4 mm (1 inch) VCR couplings. To be able to use the cell also outside the humidity generator, special consideration has to be paid to the temperature control and to sealing between the cell arms, for example, with a metal gasket as in Fig. 2a. Flat-shaped specimens such as for fabrics, packaging moisture barriers and construction materials, can be measured by putting them in place of the metal gasket between the cell arms (Fig. 2b). The cell with such a specimen is then put in the humidity generator s chamber. In this way the main advantage compared to the cup method [1,4] is that the vapor coming through the leak ports (Fig. 2b) and permeating through the side walls of the thick specimen, which are also exposed to cell surroundings the so-called boundary effect [3] is controlled. The measuring range of the setup depends on the sensitivity of the dew-point sensor and also on the flow used. Based on Eq. 2, which is explained in the following section, and the minimum dew-point range of the chilled-mirror hygrometer, the lowest WVPR that can be achieved is estimated to below 0.2 mg h 1. The low range of a permeance (see definition below) depends on the size of the exposed area of the specimen. For the tube-shaped specimen that was used in the experiments described below, the permeance can range below 1 mg m 2 day 1 hpa 1, while for the flat-shaped specimen, the lowest permeance limit would be substantially higher. 3 Governing Principles WVPR is calculated by measuring the mass flow of water-vapor through the specimen. For quasi-static methods (e.g., cup method), this means that vapor permeating through the specimen, accumulates on the dry side, since there is no mass exchange other than through the specimen. The permeation rate is determined by monitoring the change in vapor mass concentration on the dry side. For dynamic methods, vapor that permeates through the specimen increases the humidity of the carrier gas which passes the dry side at a constant flow. The mass flow of water-vapor through the specimen, ṁ perm, which is here defined as WVPR, can be found from the following relation: ṁ perm = ṁ s ṁ c, (1) where ṁ c is the incoming water-vapor mass flow in the carrier gas and ṁ s is the mass flow of the water-vapor measured by the dew-point sensor. Using the gas equation, corrected for non-ideal gas behavior, Eq. 1 can be further expressed as ṁ perm = M w V i e s (T dp,s, P s ) M w V i e s (T dp,c, P c ), (2) where M w denotes the molecular weight of water-vapor; the universal gas constant R = J mol 1 K 1 ; T i is the reference temperature used by MFC; V i is the volumetric flow rate, measured by MFC; e s (T dp,s, P s ) is the saturation pressure of water-vapor [15] att dp,s and pressure P s at the sensor, when connected to the dry

5 Int J Thermophys (2012) 33: side line (see Fig. 2), taking into account also the enhancement factor f [16]; and T dp,c and P c are the dew-point temperature and pressure of the incoming carrier gas, respectively. Equation 2 shows that for the dynamic method, WVPR is obtained from the measured flow, stable measured dew points of the incoming carrier gas, and dew-point at the sensor. This is also an assumption for most dynamic methods. However, this is not the case for low flow rates, where some steady rise of residual water-vapor concentration can be observed. Taking into account this steady rise enables a continuous relation between the quasi-static method with zero carrier-gas flow and the dynamic method with some flow present to be explained. Differentiating m s with respect to e s (T dp,s) yields an additional part: ṁ perm = M w V i e s (T dp,s, P s ) + M w d[e s V (T dp,s,p s )] dry dt M w V i e s (T dp,c, P c ), (3) where V dry is the equivalent volume of the dry side, where permeated vapor accumulates. It can be determined by finding the slope of change of the measured e s, and by solving Eq. 3 for two different e s at two different moments. The WVPR can generally be expressed in several different ways, such as mass flow, molar flow etc., however standards, which are noted in the introduction, agree on definitions of the water-vapor transmission rate (WVTR), q, the permeance, W, and the permeability, δ, as outlined in q = ṁperm A, W = ṁperm A e ṁperm,δ = d, (4) A e where A is the exposed area of the specimen, e is the difference in vapor partial pressures on each side of the specimen, and d is the thickness of the specimen. 4 Measurement Results and Uncertainty Evaluation In order to estimate the uncertainty of ṁ perm according to GUM, individual uncertainty contributions from all the components have to be evaluated and propagated through Eq. 3. Equation 3 is thus rewritten to Eq. 5 ṁ perm = M w [ Vdry B + V i ( e s (T dp,s, P s ) e s (T dp,c, P c ) )], (5) where the derivative d[e s (T dp,s,p s )] is substituted by a constant B, because small changes dt in vapor pressure exhibit nearly linear behavior, as shown in Fig. 3. Measurements were carried out on a 30 m long tube-shaped specimen, loosely coiled around the wire frame. The outer diameter was 6 mm with 1 mm of wall thickness. The wet side was set to a temperature of 20 C and 50 % relative humidity, which was alternately measured by the dew-point sensor. Each measurement point

6 1600 Int J Thermophys (2012) 33: Fig. 3 Dew-point temperature T dp,s (upper curve), measured by dew-point sensor, and calculated watervapor pressure e s (T dp,s, P s ) with plotted linear fit, at flow rate of 0.24 L min 1 at a different flow took several hours to obtain steady permeation through the specimen due to diffusion properties of the material. In all cases a steady-state resulted in a slow virtually linear drift (slope B) of vapor pressure that kept rising, because it was a part of quasi-static permeation, which would exist even with no carrier flow present. Figure 3 shows an example of such measurement for a volumetric flow of L min 1. The vapor-pressure change is calculated by fitting a straight line with slope B = Pa h 1. Table 1 shows a summary of measurement results of ṁ perm and permeance, W, for different flows and vapor pressures at the wet and dry side. The vapor pressure at the dry side is here approximated by a mid-point between e s (T dp,c, P c ) and e s (T dp,s, P s ). V dry is calculated by solving Eq. 5 for two different values of e s (T dp,s, P s ), while taking into account that ṁ perm changes proportionally to a change in the partial pressure difference between the dry and wet sides. It was found that the effect of part V dry B on ṁ perm was in fact small. The difference in the calculation of ṁ perm according to Eq. 2 and according to Eq. 5 with additional V dry B part, did not exceed 400 ppm for all different flow set points. The V dry B part was considered as an uncertainty component, which is mathematically manifested in the following transformed equation: ṁ perm = M w V i ( e RT s (T dp,s, P s ) e s (T dp,c, P c ) ) k ε,bv, (6) i where the V dry B part is replaced by a correction coefficient k ε,bv with estimated value of 1 and its relative standard uncertainty calculated according to w(k ε,bv ) = u(k ε,bv) k ε,bv assuming a uniform distribution. = = 231 ppm, (7)

7 Int J Thermophys (2012) 33: Table 1 Summary of measurement results for different flow and vapor pressure of the wet side Experiment no. Temperature of specimen ( C) Partial water-vapor pressure at wet side (Pa) Partial water-vapor pressure at dry side a (Pa) Dry gas flow (L min 1 ) WVPR (mg h 1 ) Permeance (mg m 2 day 1 hpa 1 ) a Calculated from dew-point at the beginning of steady rise of a partial pressure

8 1602 Int J Thermophys (2012) 33: The dew-point temperature of the carrier gas was measured to be below the frostpoint sensor lower limit of 55 C, which corresponds to a partial pressure e s (T dp,c, P c ) = 2.09 Pa. The true vapor pressure was estimated to be 1.05 Pa, i.e., half-way between this and zero. Assuming a uniform distribution, the standard uncertainty of this estimation is u ( e s (T dp,c, P c ) ) = 1.05 Pa/ 3 = 0.61 Pa. The dew-point measurements are traceable to a primary dew-point generator [17,18] with standard uncertainty of 0.03 C in the range from 50 Cto+20 C. Together with the measured instability of 0.02 C, the combined standard uncertainty of the dew point was C. This uncertainty is propagated through equations for water-vapor pressure according to[19], which results in a standard uncertainty of the partial pressure on the dry side, u ( e s (T dp,s, P s ) ) = 0.35 Pa. Consequently, the standard uncertainty of the partial pressure difference u ( e s (T dp,s, P s ) e s (T dp,c, P c ) ) = 0.70 Pa, which for instance at a partial pressure difference of 66.3 Pa corresponds to relative standard uncertainty of w e =1.05 %. The MFC was calibrated by comparison to a reference flow-meter in terms of a volumetric flow. The traceability of the flow measurements is not assured due to non-routine calibrations; however, for the purposes of this study the relative standard uncertainty associated with the calibration of the MFC, w( V i ), was estimated to be 1.0 %. It needs to be stressed though that the traceability of WVPR measurements will eventually depend on the traceability of flow measurements. The estimated uncertainty needs to take into account also temperature and pressure effects on the performance of the MFC. In addition, Table 1 shows a strong negative correlation, r V i, e = 0.991, between the measured flow V i and the partial pressure difference e s (T dp,s, P s ) e s (T dp,c, P c ). The gas constant R in Eq. 6 is J mol 1 K 1 with an associated standard uncertainty of 1.7 ppm [20] which is therefore negligible. The molar mass of water is taken as g mol 1 with a standard uncertainty below 1 ppm including truncating (otherwise below 1 ppb [21]) and is therefore negligible. T i is the reference temperature of the MFC, which is used to convert between the volumetric and mass flow. Its contribution in uncertainty estimation is therefore irrelevant. The temperature does have an impact on the permeation rate, but is considered as a measurement condition (specification). However, the temperature cannot be uniquely identified due to the spatial distribution across the specimen, the finite stability in time, and finally due to the uncertainty of the thermometer calibration. For our measurement setup, all these contributions account for a standard uncertainty u(t a ) = 0.18 C. For this reason an additional measurement of ṁ perm was carried out at an increased ambient temperature t a by t a = 2 C. In order to assess the temperature effect independently, the partial vapor pressure of the wet side was kept the same by decreasing the relative humidity. Experiment no. 6 in Table 1 shows a small change of ṁ perm from the average of the first four experiments ṁ perm,1 4. The relative standard uncertainty due to the temperature measurement is calculated according to w ( ṁ perm,ta ) = ṁ perm,6 ṁ perm,1 4 ṁ perm,1 4 u(t a ) t a = % (8)

9 Int J Thermophys (2012) 33: Table 2 Uncertainty budget for WVPR at temperature of C and when the vapor pressure at the wet and the dry side is 1177 Pa and 67.3 Pa, respectively; specimen was tube-shaped with dimensions of 30 m 6mm 1mm Uncertainty Relative standard component uncertainty (%) Vapor changing accumulation part, w ( ) k ε,bv Dry gas flow measurements, w ( ) V i 1.0 Partial pressure difference w e 1.05 Correlation between flow and p.p. difference, r V i, e w ew( V i ) Temperature measurements, w ( ) ṁ perm,ta Combined standard relative uncertainty 1.47 Rounded expanded relative uncertainty (k = 2) 3.0 A note should be made that the temperature might, however, have a different effect on the water-vapor transmission rate, on the permeance, and on the permeability. The atmospheric pressure has no observed impact on ṁ perm, as it would have, for instance, with the quasi-static method [3]. This can be explained by the fact that the humidity generator regulates the temperature and relative humidity regardless of the atmospheric pressure variations. In addition, the thickness of the tube wall (1 mm) is very small compared to the tube s length (30 m). For these reasons, the permeation from the side of the specimen (boundary effect) and uncertainty associated with this effect is assumed negligible. Taking into account the uncertainty contributions above, the combined standard uncertainty is calculated by w c (ṁ perm ) = u(ṁ perm) ṁ perm = w 2 (k ε,bv ) + w 2 ( V i ) + w e 2 2r Vi, e w ew( V i ) + w 2 ( ) ṁ perm,ta (9) Table 2 shows the example of the uncertainty budget for WVPR at a vapor pressure at the wet side of 1177 Pa, and 67.3 Pa at the dry side, the specimen was tube-shaped with dimensions of 30 m 6mm 1 mm. 5 Discussion Although the V dry B part in Eq. 5 or Eq. 3 became detectable because of the use of a relatively long specimen, experiments show that this contribution is relatively small compared to the total uncertainty. The measurements and uncertainty analysis showed that besides the humidity measurements, the flow measurements are very important, when dealing with the dynamic method of WVPR determination. In this paper only the total uncertainty of the MFC calibration, which is relevant for the uncertainty estimation, was expressed. In order to obtain this estimation, one needs to consider, however, also the effects of the

10 1604 Int J Thermophys (2012) 33: temperature, pressure, and density of the gases used on the flow measurements and the MFC performance. The uncertainty evaluation of the permeance, water-vapor transmission rate, and permeability was not carried out, even though most of the steps, apart from measurement of the exposed area, would practically be the same. 6 Conclusions This paper shows an uncertainty evaluation of the measurement setup for WVPR measurements. Experiments show that even though the physical model accounts for the changing accumulation part of the dynamic method, this contribution is relatively small compared to the total uncertainty. However, because this part appears as an obvious link between the quasi-static model and the dynamic model, it does require further investigation. In addition, the effect of nitrogen used as a carrier gas on the dry side compared to the effect of the air that was otherwise used on the wet side, should be further studied. The experimental relative expanded uncertainty (k = 2)for WVPR measurement of 3.0 % in the current example provides a sound basis for development of a reference facility in our national laboratory for temperature and humidity measurements. Acknowledgments This study was partially supported by the Ministry of Economic Development and Technology, Metrology Institute of Republic Slovenia in the scope of contract /2008/70 for national standard laboratory for the field of thermodynamic temperature and humidity. References 1. E.A. McCullough, M. Kwon, H. Shim, Meas. Sci. Technol. 14, 1402 (2003) 2. B. Duncan, K. Urquhart, S. Roberts, Review of Measurement and Modelling of Permeation and Diffusion in Polymers, NPL Report DEPC MPR 012 (2005) 3. K.K. Hansen, in Proceedings of the 2nd Symposium, Building Physics in the Nordic Countries, Trondheim, 1991, p M.K.Kurman,J.Build.Phys.22, 349 (1999) 5. M.K. Kumaran, J Test. Eval. 34, 241 (2006) 6. P. Mukhopadhyaya, K. Kumaran, J. Lackey, D. Reenen, J. ASTM Int. 4, 1 (2007) 7. M. Pazera, M. Salonvaara, J. Build. Phys. 33, 45 (2009) 8. G.E. Scace, W.W. Miller, Int. J. Thermophys. 29, 1544 (2008) 9. ISO , Plastics Film and sheeting Determination of Water Vapour Transmission Rate Part 1: Humidity Detection Sensor Method (2003) 10. ISO 21129, Hygrothermal Performance of Building Materials and Products Determination of Water- Vapour Transmission Properties Box Method (2007) 11. ISO 12572, Hygrothermal Performance of Building Materials and Products Determination of Water Vapour Transmission Properties (2001) 12. ASTM E96/E96M-05 Standard Test Methods for Water-Vapor Transmission of Materials (2005) 13. ISO/IEC Guide 98-3:2008, Uncertainty of Measurement Part 3: Guide to the Expression of Uncertainty in Measurement (ISO, Geneva, 2008) 14. M. Heinonen, M. Vilbaste, Int. J. Thermophys. 29, 1589 (2008) 15. D. Sonntag, in Papers and Abstracts from the Third International Symposium on Humidity and Moisture, vol. 1 (National Physical Laboratory, Middlesex, 1998), p L. Greenspan, J. Res, Natl. Bur. Stand. 80, 41 (1976) 17. D. Hudoklin, J. Bojkovski, J. Nielsen, J. Drnovšek, Measurement 41, 950 (2008)

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