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Investigation of gas permeation through Al-metallized film for vacuum insulation panels
International Journal of Heat and Mass Transfer 56 (2013) 436–446
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Investigation of gas permeation through Al-metallized film for vacuum insulation panels Haeyong Jung, Choong Hyo Jang, In Seok Yeo, Tae-Ho Song ⇑ School of Mechanical, Aerospace and System Engineering, Korea Advanced Institute of Science and Technology, Guseong-dong 373-1, Yuseong-gu, Daejeon, Republic of Korea
a r t i c l e
i n f o
Article history: Received 22 December 2011 Received in revised form 20 August 2012 Accepted 9 September 2012 Available online 27 October 2012 Keywords: Vacuum insulation panel Gas permeability Pin-hole Al-metallized film
a b s t r a c t Recently, vacuum insulation panels (VIPs) become a key issue to save the building energy. VIPs must have a good insulation performance and a long service life. Al-metallized film can meet these requirements by suppressing both of thermal bridging and gas permeation. In this work, gas permeabilities through an Almetallized film for various gases are measured using a newly-developed experimental apparatus based on a pressure difference method. Its reliability is validated by measuring a few well-known gas permeabilities through uncoated 12 lm polyethylene terephthalate (PET) film. Then, a 12 lm PET film coated with a 33 nm aluminum layer is chosen as the sample metallized film. It is confirmed by residual gas analyzer (RGA) that nitrogen, oxygen, carbon dioxide and water vapor are the major gases permeating through the Al-metallized film, which are then taken as the test gases. Permeabilities of these gases through the Al-metallized film are measured to be only about 4.1% of those through uncoated PET film. Nevertheless, it is still higher than those of metal sheets because of the abundant pin-holes. Pin-holes are investigated for the distribution and the diameter by an optical microscope. An effective gas permeability including the pin-hole effect is calculated to be 3.6–4.0% of uncoated PET film permeability, agreeing well with the experimental results. Multiple Al-metallized layers must be thus employed to be effective gas barriers. A correlation for the permeation through a layer of Al-metallized film is also derived. These research results and methods can be usefully applied to actual VIP envelope materials with multiple Al-layers. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Up to 40% of worldwide energy is spent for heating, ventilating and air conditioning of buildings (HVAC) [1]. Thermal insulation of buildings is thus becoming a key element to improve the global energy utilization efficiency and to reduce CO2 emission. While most insulation materials are developed in the early 20th century, their insulation performances are stagnant at the level of 30 mW/m K of thermal conductivity almost for a century. If we can develop an excellent insulator, this is the most promising solution to cope with the above problems. This gives impetus to the development of vacuum insulation panels (VIPs). Thermal resistance of these days’ VIP is about ten times greater than those of conventional insulation materials such as polystyrene and polyurethane foams at the same thickness. This means that much thinner insulation layer can save both of energy and building space. This will enable the existing buildings to reduce HVAC energy too through an affordable renovation.
⇑ Corresponding author. Tel.: +82 42 350 3032; fax: +82 42 350 3210. E-mail address: [email protected] (T.-H. Song). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.09.013
VIPs have to have a good insulation performance and a long service life. The evacuated space of VIPs must maintain vacuum to retain the insulation performance as long as possible. For this purpose, most VIPs are enveloped using laminated films of aluminum and polymer. A typical structure with Al-foil is shown in Fig. 1. There are two types of envelopes depending on whether it includes an Al-foil or Al-metallized film [2]. Al-foil has about 5 lm of thickness and Al-metallized layer is only about 30 nm thick. The former is prone to edge conduction as depicted in Fig. 2, since the Al-foil has very high thermal conductivity and relatively large thickness. This is a big hindrance for the performance of VIPs. The edge conductivity (contribution to the overall thermal conductivity) can be calculated by the following equation (3).
keff ; edge cond: ¼
4kAl dAl ; W
ð1Þ
where kAl and dAl are the thermal conductivity and the thickness of Al-layer, respectively. For example, for a 30 cm(W) 30 cm(W) 1 cm VIP, the edge conductivity is calculated as 13.3 mW/m K for the envelope using 5 lm-thick Al-foil, while it is drastically decreased to 0.08 mW/m K when using 30 nm-thick
H. Jung et al. / International Journal of Heat and Mass Transfer 56 (2013) 436–446
437
Nomenclature A a b C D d F j K k L M m00 N n P Q q R Ru S T
area, m2 correction factor solubility, 1/Pa mass fraction diffusivity, m2/s diameter, m weighting factor (Eq. (21)) dissociation constant gas permeability, m2/s Pa if not specified thermal conductivity, W/m K length, m the number of layers of Al-coating mass flux, kg/m2 s distribution of pin-holes, m2 number of moles pressure, N/m2 gas permeation rate, m3/s if not specified heat transfer rate, W random number universal gas constant, 8.31 J/mol K shape factor, m temperature, K
t V
v0 W
time, s volume, m3 volume of 1mole gas at 1 atm/23 °C, m3/mol width, m
Greek symbols b Kreal/KPET (Eq. (16)) d thickness, m /1 dimensionless area fraction of pin-holes dimensionless thickness of base film /2 q medium density, kg/m3 Subscripts Al aluminum eff effective h high l low p permeation PET polyethylene terephthalate uc unit cell
Fig. 1. Structure of an Al-foil envelope for VIPs (SEM photography).
Fig. 2. Edge conduction along the envelope of VIPs.
Al-metallized film. The effective thermal conductivity at the center of most VIPs is about 3 mW/m K. Therefore, it is strongly recommended to use the Al-metallized envelope especially when W is small. Unfortunately, Al-metallized films have many pin-holes which are the major gas permeation paths. Since thicker coatings yield less pin-holes, minimization of edge conduction and reduction of gas permeation through the surface of envelopes are contradictory with each other. To find the optimal solution, measurement of gas permeability through the Al-metallized film is highly required and methods to reduce the gas permeation must be developed. Many experimental apparatuses are introduced to measure the gas permeability of various materials in earlier studies. Flaconneche et al. [4] measured gas permeabilities of low density polyethylene (LDPE) and medium density polyethylene (MDPE)
using a mass spectrometer. Yeom et al. [5,6] developed a permeation apparatus using a gas chromatography (GC) and measured gas permeabilities through polymers. Nigara et al. [7,8] also used GC in the measurement of hydrogen permeability through crystals. Hino et al. [9] measured the helium permeability through SiC/SiC composite using vacuum gauges. However, these researches were performed for relatively high permeability or at high temperature. Also, they studied gas permeability for only hydrogen through metals or metallized films [10–12]. The other gas permeabilities through Al-metallized films are very low and it must be measured at the room temperature to be applied to VIPs. Therefore, an experimental apparatus having higher sensitivity is required. The purpose of this study is to compose a new experimental apparatus to measure very low gas permeabilities through the Al-metallized film for various gases at the room temperature. The
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results are going to be discussed to find the permeation mechanism. Permeation process is also simulated numerically to find a correlation of permeability through Al-metallized layers.
2. Experimental permeation apparatus and method 2.1. Experimental apparatus The experimental permeation apparatus of this study is based on the pressure difference method [13]. Its schematic diagram and photograph are shown in Fig. 3. The sample film is located between the low and the high pressure sides. A pure test gas is introduced to the high pressure side and then it is permeated to the low pressure side through the sample film. The pressure increase in the low pressure side is measured and recorded by a vacuum gauge with the time and the pressure increase rate is obtained. It is finally converted to the gas permeability. Total system is made of stainless steel and every joint is sealed with a copper gasket of 2.75 in. conflate flange to minimize the leakage, permeation and outgassing from the metals. The apparatus is initially evacuated by a mechanical and diffusion pump set to higher than 103 Pa. CVM-201Ò gauges from Scientific Instrument Service, Inc. measures pressure level of the high pressure side, and a CMR-261Ò gauge for H2O and PKR-251Ò gauge for other
gases from Pfeiffer Vacuum are installed as the vacuum gauges in the low pressure side. These two kinds of vacuum gauges are employed since the PKR-251Ò gauge is used only for dry gases. The residual gas analyzer 100 (RGA 100Ò) from Stanford Research Systems is adopted to investigate the species of permeating gases through the sample film. In the gas permeation cell, vacuum grease is applied to prevent leakage between the sample film and the copper gaskets. Stainless steel meshes are employed to avoid deformation of the sample film by the pressure difference. Two gas permeation cells are employed to increase the total permeation area (6.47 102 m2). Inner volume of the low pressure side is composed of vacuum gauges and conflate flange as shown in Fig. 3 and they are 1.22 104 m3 for H2O and 1.36 104 m3 for the other gases. This difference comes from the volume of the installed gauges. 2.2. Experimental procedure All experiments in this study are carried out in a constant temperature and constant humidity room at 23 °C and R.H. 50%. The experimental procedure is as follows: (i) After assembly, total system is evacuated by vacuum pumps. (ii) Gas permeation cells are baked at 80 °C for 24 h to minimize the outgassing.
Fig. 3. Schematic diagram and photograph of the experimental permeation apparatus.
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(iii) After cooling, the valve between the high pressure side and the vacuum pumps is closed. (iv) The test gas is introduced to the high pressure side through a variable leak valve, which can control gas flow rate, and then all valves in high pressure side are closed. (v) The valve between the low pressure side and the vacuum pumps is closed so that permeation occurs from the high to the low pressure sides only through the sample film. (vi) Pressure change in the low pressure side is measured and recorded for each test gas with the time. For the measurement of H2O permeability, the experimental apparatus and procedure must be modified because water vapor at 1 atm condenses at room temperature. CVM-201Ò gauges in the high pressure side are removed and viewports are installed instead. Also, CMR-261Ò gauge is employed instead of PKR-251Ò gauge in the low pressure side. Pure water is injected to the high pressure side instead of procedure (iv). Then, it is vaporized to its saturation pressure in the high pressure side. This process is checked through viewports. 2.3. Gas permeability correlation The gas permeation rate Q for species i is expressed in the following equation (14).
Ap 1=j 1=j Q ¼ Ki Pi;h Pi;l ðtÞ ; d
ð2Þ
where Ki is the gas permeability, Ap is the permeation area, d is the thickness of the sample film, Ph and Pl are the pressures of the high and the low pressure sides and j is the dissociation constant. It is 2 for diatomic gases in metals (due to dissociation before diffusion), and 1 for other cases. The underlying physics of Eq. (2) is that the Fickian diffusion rate across a layer is proportional to the concentration difference across it and the surface concentrations are simply the solubility multiplied by Pi,h1/j or Pi,l1/j. It is thus straight forward to derive Eq. (2) for a uniform medium, and it can be shown to be valid for a medium of non-uniform layers. As an example, think of a two-layer medium. The values of j for these layers are j1 and j2, respectively. For each layer, we may set the follow equality at a steady state.
m00i ¼
qi;1 Di;1 L1
ðC i;A C i;B Þ ¼
qi;2 Di;2 L2
ðC i;C C i;D Þ;
m00i ,
ð3Þ
where qi, Di and Ci are the mass flux, the density, the diffusivity and the mass fraction, respectively. Suppose there is a small gas volume between B and C as shown in Fig. 4. As far as this volume is agitated perfectly, Ci,B and Ci,C should be same as earlier no-volume case. If this is not met, we may devise a perpetual diffusion device which can separate a species without any work (see Fig. 5 for the illustration). Initially, Pi,1 = Pi,2 (equilibrium state). If the interface 1=j 1=j between B and C makes, C i;B – bi;1 P i;1 1 and C i;C – bi;2 Pi;2 2 (bi is the solubility), diffusion from A to B occurs then through C and D, to make Pi,1 – Pi,2 eventually. To avoid this contradiction, the equilibrium concentration is independent of the other medium in contact.
Fig. 4. Schematic of the diffusion process.
Thus, when we set up an imaginary gas volume between B and C with pressure Pi,m, the local thermodynamic equilibrium (LTE) concentrations at B and C should be such that, 1=j
1=j
C i;B ¼ bi;1 Pi;m1 ;
C i;C ¼ bi;2 Pi;m2 :
ð4Þ
These indeed make the Gibbs potentials of the three phases equal to each other. Now, we have, 1=j
m00i ¼
1=j
P i;h 1 Pi;m1 bi;1 L1
qi;1 Di;1
1=j
¼
1=j2
Pi;m2 Pi;l bi;2 L2
:
ð5Þ
qi;2 Di;2
This yields Eq. (2) under the condition j1 = j2. This argument can be extended to more-than-two-layer media to end up with Eq. (2) again for a non-uniform medium but with constant j. The mole number ni of gas in the low pressure side can be calculated as, assuming ideal gas behavior,
Pi ðtÞV ¼ ni ðtÞRu T;
ð6Þ
where P(t) is the pressure and V is the inner volume of the low pressure side, Ru is the universal gas constant and T is the absolute temperature. The increase rate ni is equal to the gas permeation rate Q as,
dni Q ; ¼ dt v0
ð7Þ
where v0 is volume of 1mole gas at 1 atm 23 °C. Eq. (2) is substituted to Eq. (7). Then,
dni 1 Ap 1=j Ki ¼ Pi;h P1=j i;l ðtÞ : dt v0 d
ð8Þ
The pressure increase rate of the low pressure side is determined as,
dPi;l 1 Ap Ru T 1=j Pi;h P1=j Ki ¼ i;l ðtÞ : dt v0 d V
ð9Þ
The pressure difference between low and high pressure sides is assumed to be a constant DP, because variation of the pressures by permeation is negligible. Then, the gas permeability K can be obtained for j = 1 as,
Ki ¼ v0
d V 1 dPi;l : Ap Ru T DP dt
ð10Þ
2.4. Outgassing and leakage test To ensure the validity of experiments, possible outgassing and leakage of the test system must be checked. First, macroscopic leakage test through each joint is performed by 979 helium leakage detectorÒ from Varian. Total system is evacuated and helium gas is issued to each joint of the experimental apparatus. A mass spectrometer can detect the leakage through each joint by checking the helium gas. Secondly, a microscopic leakage test is carried out. All valves in the experimental apparatus are closed after the total system is evacuated to 103 Pa. This means that there is no pressure difference between the low and high pressure sides. Therefore, it is possible to check the leakage from the atmosphere to the inside of the experimental apparatus and outgassing from the inner surface of the test system itself. The pressure increase with the time is measured with and without the sample film. The pressure increase by the outgassing and leakage of the experimental apparatus are finally confirmed to be completely negligible.
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Fig. 5. A perpetual diffusion device.
H2 O
N2
H2 O2 CO2
Fig. 6. Permeation gases through Al-metallized film by RGA 100Ò.
2.5. Selection of test gases Major permeation gases through the Al-metallized film among the common gases in the air are investigated using RGA 100Ò. The low pressure side is evacuated and the high pressure side is exposed to the atmosphere. Then, the permeation gases are observed by RGA 100Ò. The result is shown in Fig. 6. It is found that hydrogen, water vapor, nitrogen, oxygen and carbon dioxide are the major permeation gases. All these gases except hydrogen are permeation-tested.
4. Results and discussion
3. Reliability test of experimental apparatus Validity of the experimental apparatus is confirmed by measuring some known gas permeabilities through PET film. Table 1 shows the reported permeabilities through PET film. There is a big difference with crystalinity, i.e., whether it is amorphous or crystalline. The permeability of water vapor is much higher than the other ones. Generally, polymers have very high permeability for water vapor due to the larger solubility and diffusivity [21]. Table 1 Reported permeabilities (KPET) of gases through PET films at 25 °C. Reference
Crytalinity
[15] [16] [17] [18]
Crystalline Crystalline Crystalline Crystalline amorphous Crystalline amorphous Crystalline
[19] [20]
A 12 lm PET film from Kolon Industries Inc. is selected as the sample for validation. It has crystalline structure. Its gas permeabilities for N2 and O2 are measured at various test pressure levels. The pressure increase rates are shown in Fig. 7 and results are summarized in Table 2 (denoted as KPET). First, it is found that the gas permeability rarely changes with the test pressure. This was also shown by Lewis and Weaver [22]. Second, the employed experimental apparatus yields reasonable results compared with the other reported data, verifying the reliability of the test system.
KPET 1015 [cm3 cm/cm2 s Pa] N2
O2
CO2
H2O
– 0.525 0.725 0.494 0.987 0.450 1.08
– 2.33 2.82 2.67 4.94 – 4.77
8.85 11.0 – 10.9 21.7 8.83 22.6
– – – – – – 11,300
4.1. Experimental results As the sample Al-metallized film, a 12 lm-thick PET film coated on one side with 33 nm-thick aluminum from Kolon Industries Inc. is selected. It uses the same PET film used for the reliability test as the substrate and the coating is made by evaporation in vacuum. The coated side is exposed to the high pressure gas as shown in Fig. 8. Their pressure increase rates are shown in Fig. 9 and its gas permeabilities are calculated using Eq. (10). The results are summarized in Table 3. Before discussing the results, the uncertainty of these measurements is derived from Eq. (10) to yield the following equation [23], dK ¼ K
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 2 @K dd @K dAP @K dV @K dT @K dP h @K dPl þ þ þ þ þ : @d K @AP K @V K @T K @P h K @P l K ð11Þ Ò
Uncertainties of AP, V, T and Pl for CMR-261 gauge are 0.002%, 0.7%, 0.4% and 0.2% respectively, which are negligibly small. However, those of d, Ph and Pl for PKR-251Ò gauge are 4%, 5% and 7% respectively, which are relatively high. PKR-251Ò gauge is calibrated by
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(a)
(b)
1500
1500
ΔP = 13.2 kPa ΔP = 65.3 kPa
900
dP = 8.73 Pa/h dt ΔP =13.2 kPa
600
300
dP = 129 Pa/h dt ΔP = 40.0 kPa
1200
dP = 36.2 Pa/h dt ΔP =65.3 kPa
Pressure(Pa)
Pressure(Pa)
1200
ΔP = 14.1 kPa ΔP = 40.0 kPa
900
600
dP = 48.9 Pa/h dt ΔP =14.1 kPa
300
0 0
10
20
30
40
0 0
10
Time(hour)
20
30
Time(hour)
Fig. 7. Pressure increase rates for (a) N2 and (b) O2 through the PET film.
Table 2 Gas permeabilities (KPET) of O2 and N2 through the PET film at 23 °C. KPET 1015 [cm3 cm/cm2 s Pa]
Refs. [16–19] DP = 13.2 kPa DP = 14.1 kPa DP = 40.0 kPa DP = 65.3 kPa
N2
O2
0.450–0.725 0. 421 (±0.0311) – – 0. 353 (±0.0251)
2.33–2.82 – 2.21 (±0.157) 2.06 (±0.146) –
Fig. 8. Schematic diagram of the Al-metallized film need in the exeriments.
capacitance diaphragm gauges 690A13TRAÒ and 310CHS-1Ò from MKS instruments, Inc. at Korea Research Institute of Standards and Science (KRISS). It is known that the uncertainty of PKR-251Ò keeps linearity within 3% from the results. Pl is substituted to Eq. (10) by a linear fitting. It has a small effect on the uncertainty. Overall, these measurements have at most 7% uncertainty. The reason why the graph of the pressure in Fig. 9 is more or less parabolic initially is due to outgassing from the film surface. The effect of outgassing is negligible for the PET film for the cases of Fig. 7 because it has relatively high gas permeability, so that the rapid inner pressure increase makes the marginal outgassing fairly invisible. However, its effect is shown clearly in the Al-metallized PET film due to its very low gas permeability and inner pressure rise. The gas generation by outgassing does not sustain any more after releasing all of the residual gas in films. Therefore, the graph becomes linear in Fig. 9 after a while. This phenomenon appears only in N2 graph, but not for graphs of O2 and CO2 due to their high gas permeabilities. The H2O graph is linear in the early stage and then it becomes parabolic because it has a very high gas permeability compared with other gases. More specially, from Eq. (9), if it is solved including Pi,l1/j(t) in the right hand side (this is neglected in this study because it has very small value compared with Pi,h1/j), Pi,l(t) can be exactly calculated for j = 1 by the following equation.
1 Ap R u T t : Pi;l ðtÞ ¼ Pi;h 1 exp K i v0 d V
ð12Þ
The H2O graph can be explained by taking relatively large t in this equation. Of course, this solution reduces to Eq. (10) when t is very small. Permeabilities through the Al-metallized film with various test gases are averaged as 0.0412KPET. It is known that the gas permeability through metals is almost zero (except for hydrogen) when compared with those through polymers at room temperature [24]. The experimental results show that the gas permeability through the Al-metallized film is only about 4.1% of KPET. Though small compared with KPET, it is still high for practical applications. The reason is that the Al-metallized film has many pin-holes, which are formed in the coating process. The formation mechanism is not clearly known yet. Furthermore, it can also have scratch tracks. It is necessary to examine the pin-holes more in detail. First, distribution of pin-holes is investigated using an optical microscope. A light source is located under the Al-metallized film and the optical microscope observes the upper side. A typical image is shown in Fig. 10. The average diameter of pin-holes is 6.48 lm and its distribution is 229 ea/mm2. Assuming that pin-holes are the only gas permeation passage and they are uniformly distributed, the permeation geometry can be simplified as shown in Fig. 11. A shape factor through a thin circular disk to a semi-infinite medium is taken as [25]
S ¼ 2d;
ð13Þ
where d is the average diameter of pin-holes. The effective gas permeability is then expressed as
K eff ¼ S
d K PET ; Auc
ð14Þ
where Auc is the area of unit cell including one pin-hole and KPET is the gas permeability of pure PET film. From Eq. (14), the effective gas permeability is calculated as 0.0356KPET. However, the PET layer is not the semi-infinite medium as idealized in Fig. 11. The shape factor S is alternatively obtained numerically using the commercial code FluentÒ (this is need extensively in this study) to finally give the permeability as 0.0398KPET, to yield a minor change.
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(a)
(b)
300
dP = 2.72 Pa/h dt ΔP =92.2 kPa dP = 0.866 Pa/h dt ΔP = 27.5 kPa
100
ΔP = 27.8 kPa ΔP = 96.5 kPa
800
Pressure(Pa)
200
Pressure(Pa)
1000
ΔP = 27.5 kPa ΔP = 92.2 KPa
dP = 18.1 Pa/h dt ΔP =96.5 kPa
600
400
dP = 4.50 Pa/h dt ΔP = 27.8 kPa
200
0
0 0
20
40
0
60
(c)
1600
20
30
40
50
Time(hour)
(d)
ΔP = 34.9 kPa ΔP = 42.1 kPa
1400
2000
ΔP = 2.84 kPa
1600
1200 1000
dP = 25.6 Pa/h dt ΔP = 42.1 kPa
800 600 400
dP = 21.2 Pa/h dt ΔP =34.9 kPa
200
Pressure(Pa)
Pressure(Pa)
10
Time(hour)
1200
dP = 2673 Pa/h dt ΔP = 2.84 kPa
800
400
0
0 0
20
40
60
0.0
0.2
0.4
0.6
Time(hour)
Time(hour)
Fig. 9. Pressure increase rates for (a) N2, (b) O2, (c) CO2 and (d) H2O through the Al-metallized film.
Table 3 Gas permeabilities of O2, N2, CO2 and H2O through the Al-metallized film at 23 °C. Gases
DP
K 1015 [cc(gas@STP) cm(thickness)/cm2(area) s Pa (DP)] PET film (average value from Refs. [15–20])
Al-metallized film (measured value)
N2
27.5 kPa 92.2 kPa
0.549
0.0201 (±0.00143) 0.0188 (±0.00134)
O2
27.8 kPa 96.5 kPa
2.61
0.103 (±0.00733) 0.120 (±0.00849)
CO2
34.9 kPa 42.1 kPa
9.90
0.387 (±0.0275) 0.388 (±0.0275)
H2O
2.84 kPa
11,300
538 (±35.2)
4.2. Multiple layers of Al-coating It is clear that single coating is not practically useful for VIPs. If multiple layers of Al-coating are employed as shown in Fig. 12, the permeation rate is reduced significantly. This configuration is very useful and deserves further investigation. If both sides of the base film are Al-metallized as shown in Fig. 12(a), it is very unlikely that upper and lower pin-holes are aligned. Therefore, the effective gas permeability is expected to be significantly lower. The permeation rate can be again predicted using numerical computation.
Fig. 10. Distribution of pin-holes in the Al-metallized film by an optical microscope.
Considering computational capability, ten pin-holes are randomly distributed in each of the upper and the lower layers as shown in Fig. 13. Their coordinates are decided by random number as
x ¼ LRx ;
y ¼ LRy ;
ð15Þ
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is a dimensionless thickness of base film. In most cases, /1 is much smaller than 1. When /2 is very large, the film behaves like a semi-infinite medium [25]. This situation is similar to Eq. (14) with S in Eq. (13), so that
b1 ¼ Ndd ¼ /1 /2 ;
Fig. 11. Schematic diagram of permeation passage in the Al-metallized film.
where Rx and Ry are the random numbers lying between 0 and 1. Side walls are in adiabatic boundary condition. Parameters of pinholes from the tested film are used in this calculation. Twenty cases are calculated and the maximum and minimum results are 0.0173KPET and 0.0154KPET, respectively. They are averaged as 0.0162KPET with a standard deviation 0.0008KPET. The effective gas permeability is remarkably decreased compared with the earlier single-side Al-metallized film. For this case, the ratio b of mass fluxes of the pure base film and the both sides Al-metallized film is also investigated numerically.
b¼
K real ; K PET
ð16Þ
where Kreal is the permeability through double-side Al-metallized film. It is a function of the diameter, the distribution of pin-holes and thickness of the base film. They are nondimensionalized by the Buckingham p theorem as [26]
2 d b ¼ f Nd ; ¼ f ð/1 ; /2 Þ; d
2
/1 ¼ Nd ;
d /2 ¼ ; d
ð17Þ
where N [ea/m2] is the number distribution of pin-holes. The dimensionless variable /1 is an area fraction of pin-holes and /2
ð18Þ
This is also confirmed by numerical calculations. The effects of pinhole locations are investigated as shown in Fig. 14 and their results are summarized in Table 4. For smaller /1 and bigger /2, the numerical result approaches this theoretical limit. The effects of mis-alignment and multiple pin-holes are less than a few percent when /1 = 0.0001. Therefore, their effects can be neglected when /1 1 and /2 1. On the other hand, when the dimensionless thickness of base film /2 is very small, it can be treated as two-dimensional diffusion between small disks. This case is simplified as shown in Fig. 15 assuming a uniform distribution of pin-holes. This is approximated pffiffiffiffiffiffiffiffiffiffi by concentric diffusion with equivalent radius 1= 2pN [27]. The ratio b becomes then b2 as
b2 ¼
pNd2
ln
qffiffiffi 2
1
p2
2
p/1 /22
¼
ln Nd
ln
qffiffiffi 2
1
p2
:
ð19Þ
ln /1
However, this approximation needs a correction factor due to the ‘‘concentric diffusion’’ simplification. For intermediate values of /2, the ratio b may be expressed by a combination of b1 and b2. Therefore, correlation for this case is developed through numerous numerical simulations. Forty cases of ratios of mass fluxes are calculated with /1 = 0.01, 0.005, 0.003, 0.001 and /2 = 0.1, 0.3, 0.5, 1.0, 3.0, 5.0, 10, 30, 50, 100, respectively. Ten pin-holes on each layer are also considered as
Fig. 12. Schematic diagram of multiple layers of Al-coating.
Fig. 13. Schematic diagram for calculation of the effective gas permeability with both sides of Al-coating and randomly distributed pin-holes.
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(a) a pair of aligned pin-holes
(b) a pair of mis-aligned pin-holes
(c) two pairs of aligned pin-holes
(d) ten pairs of randomly distributed pin-holes
Fig. 14. Schematic diagram for numerical investigation of effects of mis-alignment of pin-holes.
Table 4 The effects of mis-alignment of pin-holes in Fig. 12. Pin-hole(s) arrangement
(a) A pair, aligned (b) A pair, misaligned (c) Two pairs, aligned (d) Ten pairs, randomlydistributed
b /1 = 0.001, /2 = 100
/1 = 0.0001, /2 = 100
Theoretical analysis
Numerical analysis
Theoretical analysis
Numerical analysis
0.1 0.1
0.0940 0.0923
0.01 0.01
0.00995 0.00987
0.1
0.0935
0.01
0.00992
0.1
0.0924
0.01
0.00972
2
3 n o /2 p / 6 7 qffiffiffi 2 b ¼ /1 /2 4 þ 1:97 tan1 ð/2 e0:0201/2 Þ 5: 10000/1 þ /2 2 ln 2 1 ln/ p
2
1
ð21Þ
before and their results are summarized in Table 5. The correlation for the ratio of mass fluxes is proposed as
b ¼ F 1 b1 þ aF 2 b2 ;
where a is the correction factor of b2, F1 and F2 are weighting factors of b1 and b2 respectively. Factor F1 increases from 0 to 1 and F2 decays from 1 to 0 with increasing /2, because b converges to ab2 with decreasing /2 and it converges to b1 with increasing /2 as mentioned before. It is confirmed, from the 40 numerical results, that F1 is a function of /1 and /2 and F2 is a function of /2 only. Finally, we propose the following correlation,
ð20Þ
To check the validity, the earlier test case of Fig. 13 (/1 = 0.00962, /2 = 1.85) is calculated as b = 0.0152 by this correlation. This is close to the numerical prediction b = 0.0162. More tests show that this correlation is reliable within 10% error. For further improvement, more than two Al-layers may be employed as shown in Fig. 12(b). In this case, each pair of neighboring Al-layers may be considered as a serially-connected diffusion resis-
Fig. 15. Simplification of diffusion between upper and lower pin-holes when /2 1.
21.7 12.7 3.42 +3.19 +6.44 +1.84 4.90 16.1 16.2 7.28 9.97 106 7.89 105 1.92 104 5.64 104 2.36 103 4.40 103 9.98 103 3.25 102 5.28 102 9.91 102 13.8 3.75 +1.19 +8.97 +14.0 +13.0 +11.3 0.493 5.11 +3.88 3.34 105 2.63 104 6.33 104 1.81 103 6.86 103 1.20 102 2.55 102 8.12 102 1.34 101 2.60 101
8.19 106 7.00 105 1.86 104 5.83 104 2.53 103 4.48 103 9.51 103 2.80 102 4.55 102 9.24 102
Relative error (%) Correlation Numerical simulation Relative error (%) Correlation
0.001
H. Jung et al. / International Journal of Heat and Mass Transfer 56 (2013) 436–446
445
tance. Therefore, a three Al-layers film can be treated as two double-side-coated films. More specially, when these are M + 1 coating layers (thus M PET layers between them), the permeation rate is reduced inversely proportional to M. In conclusion, more than two Al-layers have to be employed to efficiently block the gas permeation. 5. Conclusion An experimental apparatus is invented to measure the gas permeabilities through the Al-metallized film. Its reliability is proved by comparing the measurements with some known gas permeabilities through PET films. Gas permeabilities through the Al-metallized film are measured for a 12 lm PET film coated with a 33 nm Aluminum layer. Gas permeabilities for nitrogen, oxygen, carbon dioxide and water vapor are measured to be about 0.041KPET; only about 4.1% of those through uncoated PET film. Since it is still higher than those of metal sheets, resulting from the pin-holes, the effects of pin-holes are further investigated numerically. Through extensive computations for PET film with both side coatings, a correlation for the ratio of permeation rates between pure base film and both-side Al-metallized film is proposed as a function of diameter, area fraction of pin-holes and thickness of the base film. Multiple coating layers are shown to reduce the gas permeation significantly.
2.94 105 2.53 104 6.41 104 1.99 103 7.97 103 1.38 102 2.88 102 8.08 102 1.28 101 2.71 101 12.1 2.30 +1.51 +5.47 +11.3 +12.1 +10.8 +4.26 +0.133 14.3 6.08 105 4.76 104 1.15 103 3.25 103 1.20 102 2.05 102 4.15 102 1.23 101 1.99 101 3.88 101 0.1 0.3 0.5 1.0 3.0 5.0 10 30 50 100
10.7 2.30 0.737 +4.17 +4.16 +4.39 +7.04 +4.54 +7.11 12.0 1.41 104 1.10 103 2.64 103 7.45 103 2.68 102 4.48 102 8.65 102 2.25 101 3.40 101 6.27 101 1.27 104 1.08 103 2.62 103 7.78 103 2.80 102 4.69 102 9.31 102 2.36 101 3.66 101 5.60 101
5.42 105 4.66 104 1.16 103 3.44 103 1.35 102 2.33 102 4.65 102 1.28 101 2.00 101 3.39 101
0.003
Numerical simulation
0.005
Numerical simulation Numerical simulation
Relative error (%) Correlation 0.01
/1 /2
Table 5 Kreal/KPET for both side Al-metallized film by numerical simulation and correlation.
Correlation
Relative error (%)
Acknowledgments The authors gratefully acknowledge the financial support of several projects: the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 20110027642) and the second stage of the Brain Korea 21 Project in 2011. References [1] Department of Trade and Industry, Energy Trends, London, 2003, pp. 4–23. [2] J. Fricke, H. Schwab, U. Heinemann, Vacuum insulation panels – exciting thermal properties and most challenging applications, Int. J. Thermophys. 27 (4) (2006) 1123–1139. [3] M.J. Tenpierik, J.J.M. Cauberg, T.I. Thorsell, Integrating vacuum insulation panels in building constructions: an integral perspective, Constr. Innov. Inform. Process Manage. 7 (1) (2007) 38–53. [4] B. Flaconneche, J. Martin, M.H. Klopffer, Transport properties of gases in polymer: experimental methods, Oil Gas Sci. Technol. 56 (3) (2001) 245–259. [5] C.K. Yeom, J.M. Lee, Y.T. Hong, K.Y. Choi, S.C. Kim, Analysis of permeation transients of pure gases through dense polymeric membranes measured by a new permeation apparatus, J. Membr. Sci. 166 (1) (2000) 71–83. [6] C.K. Yeom, S.H. Lee, H.Y. Song, J.M. Lee, Vapor permeations of a series of VOCs/ N2 mixtures through PDMS membrane, J. Membr. Sci. 198 (1) (2002) 129–143. [7] Y. Nigara, K. Kawamura, T. Kawada, J. Mizusaki, M. Ishigame, Hydrogen permeability in sintered CeO2 at high temperatures, J. Electrochem. Soc. 146 (8) (1999) 2948–2953. [8] Y. Nigara, K. Yashiro, J.-O. Hong, T. Kawada, J. Mizusaki, Hydrogen permeability of YSZ single crystals at high temperatures, Solid State Ionics 171 (1–2) (2004) 61–67. [9] T. Hino, E. Hayashishita, Y. Yamauchi, M. Hashiba, Y. Hirohata, A. Kohyama, Helium gas permeability of SiC/SiC composite used for in-vessel components of nuclear fusion reactor, Fusion Eng. Des. 73 (1) (2005) 51–56. [10] J.K. Gorman, W.R. Nardella, Hydrogen permeation through metals, Vacuum 12 (1) (1962) 19–24. [11] K.B. Kim, K. Park, J.S. Lee, Hydrogen permeation behavior of nickel electroplated AISI 4340 steel, Met. Mater. Int. 4 (5) (1998) 1013–1016. [12] H. Shirai, H. Tanaka, H. Sakaguchi, G. Adachi, Hydrogen permeation through various oxide/metal multilayered films, J. Phys. Chem. 97 (22) (1993) 6007– 6010. [13] J. Crank, G.S. Park, Diffusion in Polymer, Academic Press, London, 1968. pp. 4– 14. [14] A. Roth, Vacuum Technology, third ed., Elsevier, Amsterdam, 1990. pp. 149– 169. [15] D.W. Brubaker, K. Kammermeyer, Flow gases through plastic membranes, Ind. Eng. Chem. 45 (5) (1953) 1148–1152. [16] E.-A. McGonigle, J.J. Liggat, R.A. Pethrick, S.D. Jenkins, J.H. Daly, D. Hayward, Permeability of N2, Ar, He, O2 and CO2 through biaxially oriented polyester films-dependence on free volume, Polymer 42 (6) (2001) 2413–2426.
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[17] R. Waack, N.H. Alex, V. Stannett, M. Szwarc, Permeability of polymer films to gases and vapors, Ind. Eng. Chem. 47 (12) (1955) 2524–2527. [18] A.S. Michales, W.R. Vieth, J.A. Barrie, Diffusion of gases in polyethylene terephthalate, J. Appl. Phys. 34 (13) (1963) 13–20. [19] S.T. Hwang, C.K. Choi, K. Kammermeyer, Gaseous transfer coefficients in membranes, Sep. Sci. 9 (6) (1974) 461–478. [20] J. Brandup, E.H. Immergrut, E.A. Grulke, Permeability and Diffusion Data Polymer Handbook, fourth ed., Wiley, New York, 1999. pp. VI544–VI563. [21] S.J. Metz, W.J.C. van de Ven, J. Potreck, M.H.V. Mulder, M. Wessling, Transport of water vapor and inert gas mixtures through highly selective and highly permeable polymer membrane, J. Membr. Sci. 251 (1–2) (2005) 29–41.
[22] J.S. Lewis, M.S. Weaver, Thin-film permeation-barrier technology for flexible organic light-emitting devices, IEEE J. Sel. Top. Quantum Electron. 10 (1) (2004) 45–57. [23] J.P. Holman, Experimental Methods for Engineers, sixth ed., McGraw-Hill, New York, 1994. pp. 45–56. [24] F.J. Norton, Permeation of gases through solids, J. Appl. Phys. 28 (1) (1957) 34–39. [25] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, fifth ed., Wiley, New York, 2002. 192–194. [26] E. Buckingham, On physically similar systems; illustrations of the use of dimensional equations, Phys. Rev. 4 (4) (1914) 345–376. [27] I.S. Yoon, Development of a Multiple Layer Vacuum Insulation Chip, Ph.D. Thesis, Korea Advanced Institute of Science and Technology, Daejeon, 2009.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Investigation of gas permeation through Al-metallized film for vacuum insulation panels Haeyong Jung, Choong Hyo Jang, In Seok Yeo, Tae-Ho Song ⇑ School of Mechanical, Aerospace and System Engineering, Korea Advanced Institute of Science and Technology, Guseong-dong 373-1, Yuseong-gu, Daejeon, Republic of Korea
a r t i c l e
i n f o
Article history: Received 22 December 2011 Received in revised form 20 August 2012 Accepted 9 September 2012 Available online 27 October 2012 Keywords: Vacuum insulation panel Gas permeability Pin-hole Al-metallized film
a b s t r a c t Recently, vacuum insulation panels (VIPs) become a key issue to save the building energy. VIPs must have a good insulation performance and a long service life. Al-metallized film can meet these requirements by suppressing both of thermal bridging and gas permeation. In this work, gas permeabilities through an Almetallized film for various gases are measured using a newly-developed experimental apparatus based on a pressure difference method. Its reliability is validated by measuring a few well-known gas permeabilities through uncoated 12 lm polyethylene terephthalate (PET) film. Then, a 12 lm PET film coated with a 33 nm aluminum layer is chosen as the sample metallized film. It is confirmed by residual gas analyzer (RGA) that nitrogen, oxygen, carbon dioxide and water vapor are the major gases permeating through the Al-metallized film, which are then taken as the test gases. Permeabilities of these gases through the Al-metallized film are measured to be only about 4.1% of those through uncoated PET film. Nevertheless, it is still higher than those of metal sheets because of the abundant pin-holes. Pin-holes are investigated for the distribution and the diameter by an optical microscope. An effective gas permeability including the pin-hole effect is calculated to be 3.6–4.0% of uncoated PET film permeability, agreeing well with the experimental results. Multiple Al-metallized layers must be thus employed to be effective gas barriers. A correlation for the permeation through a layer of Al-metallized film is also derived. These research results and methods can be usefully applied to actual VIP envelope materials with multiple Al-layers. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Up to 40% of worldwide energy is spent for heating, ventilating and air conditioning of buildings (HVAC) [1]. Thermal insulation of buildings is thus becoming a key element to improve the global energy utilization efficiency and to reduce CO2 emission. While most insulation materials are developed in the early 20th century, their insulation performances are stagnant at the level of 30 mW/m K of thermal conductivity almost for a century. If we can develop an excellent insulator, this is the most promising solution to cope with the above problems. This gives impetus to the development of vacuum insulation panels (VIPs). Thermal resistance of these days’ VIP is about ten times greater than those of conventional insulation materials such as polystyrene and polyurethane foams at the same thickness. This means that much thinner insulation layer can save both of energy and building space. This will enable the existing buildings to reduce HVAC energy too through an affordable renovation.
⇑ Corresponding author. Tel.: +82 42 350 3032; fax: +82 42 350 3210. E-mail address: [email protected] (T.-H. Song). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.09.013
VIPs have to have a good insulation performance and a long service life. The evacuated space of VIPs must maintain vacuum to retain the insulation performance as long as possible. For this purpose, most VIPs are enveloped using laminated films of aluminum and polymer. A typical structure with Al-foil is shown in Fig. 1. There are two types of envelopes depending on whether it includes an Al-foil or Al-metallized film [2]. Al-foil has about 5 lm of thickness and Al-metallized layer is only about 30 nm thick. The former is prone to edge conduction as depicted in Fig. 2, since the Al-foil has very high thermal conductivity and relatively large thickness. This is a big hindrance for the performance of VIPs. The edge conductivity (contribution to the overall thermal conductivity) can be calculated by the following equation (3).
keff ; edge cond: ¼
4kAl dAl ; W
ð1Þ
where kAl and dAl are the thermal conductivity and the thickness of Al-layer, respectively. For example, for a 30 cm(W) 30 cm(W) 1 cm VIP, the edge conductivity is calculated as 13.3 mW/m K for the envelope using 5 lm-thick Al-foil, while it is drastically decreased to 0.08 mW/m K when using 30 nm-thick
H. Jung et al. / International Journal of Heat and Mass Transfer 56 (2013) 436–446
437
Nomenclature A a b C D d F j K k L M m00 N n P Q q R Ru S T
area, m2 correction factor solubility, 1/Pa mass fraction diffusivity, m2/s diameter, m weighting factor (Eq. (21)) dissociation constant gas permeability, m2/s Pa if not specified thermal conductivity, W/m K length, m the number of layers of Al-coating mass flux, kg/m2 s distribution of pin-holes, m2 number of moles pressure, N/m2 gas permeation rate, m3/s if not specified heat transfer rate, W random number universal gas constant, 8.31 J/mol K shape factor, m temperature, K
t V
v0 W
time, s volume, m3 volume of 1mole gas at 1 atm/23 °C, m3/mol width, m
Greek symbols b Kreal/KPET (Eq. (16)) d thickness, m /1 dimensionless area fraction of pin-holes dimensionless thickness of base film /2 q medium density, kg/m3 Subscripts Al aluminum eff effective h high l low p permeation PET polyethylene terephthalate uc unit cell
Fig. 1. Structure of an Al-foil envelope for VIPs (SEM photography).
Fig. 2. Edge conduction along the envelope of VIPs.
Al-metallized film. The effective thermal conductivity at the center of most VIPs is about 3 mW/m K. Therefore, it is strongly recommended to use the Al-metallized envelope especially when W is small. Unfortunately, Al-metallized films have many pin-holes which are the major gas permeation paths. Since thicker coatings yield less pin-holes, minimization of edge conduction and reduction of gas permeation through the surface of envelopes are contradictory with each other. To find the optimal solution, measurement of gas permeability through the Al-metallized film is highly required and methods to reduce the gas permeation must be developed. Many experimental apparatuses are introduced to measure the gas permeability of various materials in earlier studies. Flaconneche et al. [4] measured gas permeabilities of low density polyethylene (LDPE) and medium density polyethylene (MDPE)
using a mass spectrometer. Yeom et al. [5,6] developed a permeation apparatus using a gas chromatography (GC) and measured gas permeabilities through polymers. Nigara et al. [7,8] also used GC in the measurement of hydrogen permeability through crystals. Hino et al. [9] measured the helium permeability through SiC/SiC composite using vacuum gauges. However, these researches were performed for relatively high permeability or at high temperature. Also, they studied gas permeability for only hydrogen through metals or metallized films [10–12]. The other gas permeabilities through Al-metallized films are very low and it must be measured at the room temperature to be applied to VIPs. Therefore, an experimental apparatus having higher sensitivity is required. The purpose of this study is to compose a new experimental apparatus to measure very low gas permeabilities through the Al-metallized film for various gases at the room temperature. The
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results are going to be discussed to find the permeation mechanism. Permeation process is also simulated numerically to find a correlation of permeability through Al-metallized layers.
2. Experimental permeation apparatus and method 2.1. Experimental apparatus The experimental permeation apparatus of this study is based on the pressure difference method [13]. Its schematic diagram and photograph are shown in Fig. 3. The sample film is located between the low and the high pressure sides. A pure test gas is introduced to the high pressure side and then it is permeated to the low pressure side through the sample film. The pressure increase in the low pressure side is measured and recorded by a vacuum gauge with the time and the pressure increase rate is obtained. It is finally converted to the gas permeability. Total system is made of stainless steel and every joint is sealed with a copper gasket of 2.75 in. conflate flange to minimize the leakage, permeation and outgassing from the metals. The apparatus is initially evacuated by a mechanical and diffusion pump set to higher than 103 Pa. CVM-201Ò gauges from Scientific Instrument Service, Inc. measures pressure level of the high pressure side, and a CMR-261Ò gauge for H2O and PKR-251Ò gauge for other
gases from Pfeiffer Vacuum are installed as the vacuum gauges in the low pressure side. These two kinds of vacuum gauges are employed since the PKR-251Ò gauge is used only for dry gases. The residual gas analyzer 100 (RGA 100Ò) from Stanford Research Systems is adopted to investigate the species of permeating gases through the sample film. In the gas permeation cell, vacuum grease is applied to prevent leakage between the sample film and the copper gaskets. Stainless steel meshes are employed to avoid deformation of the sample film by the pressure difference. Two gas permeation cells are employed to increase the total permeation area (6.47 102 m2). Inner volume of the low pressure side is composed of vacuum gauges and conflate flange as shown in Fig. 3 and they are 1.22 104 m3 for H2O and 1.36 104 m3 for the other gases. This difference comes from the volume of the installed gauges. 2.2. Experimental procedure All experiments in this study are carried out in a constant temperature and constant humidity room at 23 °C and R.H. 50%. The experimental procedure is as follows: (i) After assembly, total system is evacuated by vacuum pumps. (ii) Gas permeation cells are baked at 80 °C for 24 h to minimize the outgassing.
Fig. 3. Schematic diagram and photograph of the experimental permeation apparatus.
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(iii) After cooling, the valve between the high pressure side and the vacuum pumps is closed. (iv) The test gas is introduced to the high pressure side through a variable leak valve, which can control gas flow rate, and then all valves in high pressure side are closed. (v) The valve between the low pressure side and the vacuum pumps is closed so that permeation occurs from the high to the low pressure sides only through the sample film. (vi) Pressure change in the low pressure side is measured and recorded for each test gas with the time. For the measurement of H2O permeability, the experimental apparatus and procedure must be modified because water vapor at 1 atm condenses at room temperature. CVM-201Ò gauges in the high pressure side are removed and viewports are installed instead. Also, CMR-261Ò gauge is employed instead of PKR-251Ò gauge in the low pressure side. Pure water is injected to the high pressure side instead of procedure (iv). Then, it is vaporized to its saturation pressure in the high pressure side. This process is checked through viewports. 2.3. Gas permeability correlation The gas permeation rate Q for species i is expressed in the following equation (14).
Ap 1=j 1=j Q ¼ Ki Pi;h Pi;l ðtÞ ; d
ð2Þ
where Ki is the gas permeability, Ap is the permeation area, d is the thickness of the sample film, Ph and Pl are the pressures of the high and the low pressure sides and j is the dissociation constant. It is 2 for diatomic gases in metals (due to dissociation before diffusion), and 1 for other cases. The underlying physics of Eq. (2) is that the Fickian diffusion rate across a layer is proportional to the concentration difference across it and the surface concentrations are simply the solubility multiplied by Pi,h1/j or Pi,l1/j. It is thus straight forward to derive Eq. (2) for a uniform medium, and it can be shown to be valid for a medium of non-uniform layers. As an example, think of a two-layer medium. The values of j for these layers are j1 and j2, respectively. For each layer, we may set the follow equality at a steady state.
m00i ¼
qi;1 Di;1 L1
ðC i;A C i;B Þ ¼
qi;2 Di;2 L2
ðC i;C C i;D Þ;
m00i ,
ð3Þ
where qi, Di and Ci are the mass flux, the density, the diffusivity and the mass fraction, respectively. Suppose there is a small gas volume between B and C as shown in Fig. 4. As far as this volume is agitated perfectly, Ci,B and Ci,C should be same as earlier no-volume case. If this is not met, we may devise a perpetual diffusion device which can separate a species without any work (see Fig. 5 for the illustration). Initially, Pi,1 = Pi,2 (equilibrium state). If the interface 1=j 1=j between B and C makes, C i;B – bi;1 P i;1 1 and C i;C – bi;2 Pi;2 2 (bi is the solubility), diffusion from A to B occurs then through C and D, to make Pi,1 – Pi,2 eventually. To avoid this contradiction, the equilibrium concentration is independent of the other medium in contact.
Fig. 4. Schematic of the diffusion process.
Thus, when we set up an imaginary gas volume between B and C with pressure Pi,m, the local thermodynamic equilibrium (LTE) concentrations at B and C should be such that, 1=j
1=j
C i;B ¼ bi;1 Pi;m1 ;
C i;C ¼ bi;2 Pi;m2 :
ð4Þ
These indeed make the Gibbs potentials of the three phases equal to each other. Now, we have, 1=j
m00i ¼
1=j
P i;h 1 Pi;m1 bi;1 L1
qi;1 Di;1
1=j
¼
1=j2
Pi;m2 Pi;l bi;2 L2
:
ð5Þ
qi;2 Di;2
This yields Eq. (2) under the condition j1 = j2. This argument can be extended to more-than-two-layer media to end up with Eq. (2) again for a non-uniform medium but with constant j. The mole number ni of gas in the low pressure side can be calculated as, assuming ideal gas behavior,
Pi ðtÞV ¼ ni ðtÞRu T;
ð6Þ
where P(t) is the pressure and V is the inner volume of the low pressure side, Ru is the universal gas constant and T is the absolute temperature. The increase rate ni is equal to the gas permeation rate Q as,
dni Q ; ¼ dt v0
ð7Þ
where v0 is volume of 1mole gas at 1 atm 23 °C. Eq. (2) is substituted to Eq. (7). Then,
dni 1 Ap 1=j Ki ¼ Pi;h P1=j i;l ðtÞ : dt v0 d
ð8Þ
The pressure increase rate of the low pressure side is determined as,
dPi;l 1 Ap Ru T 1=j Pi;h P1=j Ki ¼ i;l ðtÞ : dt v0 d V
ð9Þ
The pressure difference between low and high pressure sides is assumed to be a constant DP, because variation of the pressures by permeation is negligible. Then, the gas permeability K can be obtained for j = 1 as,
Ki ¼ v0
d V 1 dPi;l : Ap Ru T DP dt
ð10Þ
2.4. Outgassing and leakage test To ensure the validity of experiments, possible outgassing and leakage of the test system must be checked. First, macroscopic leakage test through each joint is performed by 979 helium leakage detectorÒ from Varian. Total system is evacuated and helium gas is issued to each joint of the experimental apparatus. A mass spectrometer can detect the leakage through each joint by checking the helium gas. Secondly, a microscopic leakage test is carried out. All valves in the experimental apparatus are closed after the total system is evacuated to 103 Pa. This means that there is no pressure difference between the low and high pressure sides. Therefore, it is possible to check the leakage from the atmosphere to the inside of the experimental apparatus and outgassing from the inner surface of the test system itself. The pressure increase with the time is measured with and without the sample film. The pressure increase by the outgassing and leakage of the experimental apparatus are finally confirmed to be completely negligible.
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Fig. 5. A perpetual diffusion device.
H2 O
N2
H2 O2 CO2
Fig. 6. Permeation gases through Al-metallized film by RGA 100Ò.
2.5. Selection of test gases Major permeation gases through the Al-metallized film among the common gases in the air are investigated using RGA 100Ò. The low pressure side is evacuated and the high pressure side is exposed to the atmosphere. Then, the permeation gases are observed by RGA 100Ò. The result is shown in Fig. 6. It is found that hydrogen, water vapor, nitrogen, oxygen and carbon dioxide are the major permeation gases. All these gases except hydrogen are permeation-tested.
4. Results and discussion
3. Reliability test of experimental apparatus Validity of the experimental apparatus is confirmed by measuring some known gas permeabilities through PET film. Table 1 shows the reported permeabilities through PET film. There is a big difference with crystalinity, i.e., whether it is amorphous or crystalline. The permeability of water vapor is much higher than the other ones. Generally, polymers have very high permeability for water vapor due to the larger solubility and diffusivity [21]. Table 1 Reported permeabilities (KPET) of gases through PET films at 25 °C. Reference
Crytalinity
[15] [16] [17] [18]
Crystalline Crystalline Crystalline Crystalline amorphous Crystalline amorphous Crystalline
[19] [20]
A 12 lm PET film from Kolon Industries Inc. is selected as the sample for validation. It has crystalline structure. Its gas permeabilities for N2 and O2 are measured at various test pressure levels. The pressure increase rates are shown in Fig. 7 and results are summarized in Table 2 (denoted as KPET). First, it is found that the gas permeability rarely changes with the test pressure. This was also shown by Lewis and Weaver [22]. Second, the employed experimental apparatus yields reasonable results compared with the other reported data, verifying the reliability of the test system.
KPET 1015 [cm3 cm/cm2 s Pa] N2
O2
CO2
H2O
– 0.525 0.725 0.494 0.987 0.450 1.08
– 2.33 2.82 2.67 4.94 – 4.77
8.85 11.0 – 10.9 21.7 8.83 22.6
– – – – – – 11,300
4.1. Experimental results As the sample Al-metallized film, a 12 lm-thick PET film coated on one side with 33 nm-thick aluminum from Kolon Industries Inc. is selected. It uses the same PET film used for the reliability test as the substrate and the coating is made by evaporation in vacuum. The coated side is exposed to the high pressure gas as shown in Fig. 8. Their pressure increase rates are shown in Fig. 9 and its gas permeabilities are calculated using Eq. (10). The results are summarized in Table 3. Before discussing the results, the uncertainty of these measurements is derived from Eq. (10) to yield the following equation [23], dK ¼ K
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 2 2 @K dd @K dAP @K dV @K dT @K dP h @K dPl þ þ þ þ þ : @d K @AP K @V K @T K @P h K @P l K ð11Þ Ò
Uncertainties of AP, V, T and Pl for CMR-261 gauge are 0.002%, 0.7%, 0.4% and 0.2% respectively, which are negligibly small. However, those of d, Ph and Pl for PKR-251Ò gauge are 4%, 5% and 7% respectively, which are relatively high. PKR-251Ò gauge is calibrated by
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(a)
(b)
1500
1500
ΔP = 13.2 kPa ΔP = 65.3 kPa
900
dP = 8.73 Pa/h dt ΔP =13.2 kPa
600
300
dP = 129 Pa/h dt ΔP = 40.0 kPa
1200
dP = 36.2 Pa/h dt ΔP =65.3 kPa
Pressure(Pa)
Pressure(Pa)
1200
ΔP = 14.1 kPa ΔP = 40.0 kPa
900
600
dP = 48.9 Pa/h dt ΔP =14.1 kPa
300
0 0
10
20
30
40
0 0
10
Time(hour)
20
30
Time(hour)
Fig. 7. Pressure increase rates for (a) N2 and (b) O2 through the PET film.
Table 2 Gas permeabilities (KPET) of O2 and N2 through the PET film at 23 °C. KPET 1015 [cm3 cm/cm2 s Pa]
Refs. [16–19] DP = 13.2 kPa DP = 14.1 kPa DP = 40.0 kPa DP = 65.3 kPa
N2
O2
0.450–0.725 0. 421 (±0.0311) – – 0. 353 (±0.0251)
2.33–2.82 – 2.21 (±0.157) 2.06 (±0.146) –
Fig. 8. Schematic diagram of the Al-metallized film need in the exeriments.
capacitance diaphragm gauges 690A13TRAÒ and 310CHS-1Ò from MKS instruments, Inc. at Korea Research Institute of Standards and Science (KRISS). It is known that the uncertainty of PKR-251Ò keeps linearity within 3% from the results. Pl is substituted to Eq. (10) by a linear fitting. It has a small effect on the uncertainty. Overall, these measurements have at most 7% uncertainty. The reason why the graph of the pressure in Fig. 9 is more or less parabolic initially is due to outgassing from the film surface. The effect of outgassing is negligible for the PET film for the cases of Fig. 7 because it has relatively high gas permeability, so that the rapid inner pressure increase makes the marginal outgassing fairly invisible. However, its effect is shown clearly in the Al-metallized PET film due to its very low gas permeability and inner pressure rise. The gas generation by outgassing does not sustain any more after releasing all of the residual gas in films. Therefore, the graph becomes linear in Fig. 9 after a while. This phenomenon appears only in N2 graph, but not for graphs of O2 and CO2 due to their high gas permeabilities. The H2O graph is linear in the early stage and then it becomes parabolic because it has a very high gas permeability compared with other gases. More specially, from Eq. (9), if it is solved including Pi,l1/j(t) in the right hand side (this is neglected in this study because it has very small value compared with Pi,h1/j), Pi,l(t) can be exactly calculated for j = 1 by the following equation.
1 Ap R u T t : Pi;l ðtÞ ¼ Pi;h 1 exp K i v0 d V
ð12Þ
The H2O graph can be explained by taking relatively large t in this equation. Of course, this solution reduces to Eq. (10) when t is very small. Permeabilities through the Al-metallized film with various test gases are averaged as 0.0412KPET. It is known that the gas permeability through metals is almost zero (except for hydrogen) when compared with those through polymers at room temperature [24]. The experimental results show that the gas permeability through the Al-metallized film is only about 4.1% of KPET. Though small compared with KPET, it is still high for practical applications. The reason is that the Al-metallized film has many pin-holes, which are formed in the coating process. The formation mechanism is not clearly known yet. Furthermore, it can also have scratch tracks. It is necessary to examine the pin-holes more in detail. First, distribution of pin-holes is investigated using an optical microscope. A light source is located under the Al-metallized film and the optical microscope observes the upper side. A typical image is shown in Fig. 10. The average diameter of pin-holes is 6.48 lm and its distribution is 229 ea/mm2. Assuming that pin-holes are the only gas permeation passage and they are uniformly distributed, the permeation geometry can be simplified as shown in Fig. 11. A shape factor through a thin circular disk to a semi-infinite medium is taken as [25]
S ¼ 2d;
ð13Þ
where d is the average diameter of pin-holes. The effective gas permeability is then expressed as
K eff ¼ S
d K PET ; Auc
ð14Þ
where Auc is the area of unit cell including one pin-hole and KPET is the gas permeability of pure PET film. From Eq. (14), the effective gas permeability is calculated as 0.0356KPET. However, the PET layer is not the semi-infinite medium as idealized in Fig. 11. The shape factor S is alternatively obtained numerically using the commercial code FluentÒ (this is need extensively in this study) to finally give the permeability as 0.0398KPET, to yield a minor change.
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(a)
(b)
300
dP = 2.72 Pa/h dt ΔP =92.2 kPa dP = 0.866 Pa/h dt ΔP = 27.5 kPa
100
ΔP = 27.8 kPa ΔP = 96.5 kPa
800
Pressure(Pa)
200
Pressure(Pa)
1000
ΔP = 27.5 kPa ΔP = 92.2 KPa
dP = 18.1 Pa/h dt ΔP =96.5 kPa
600
400
dP = 4.50 Pa/h dt ΔP = 27.8 kPa
200
0
0 0
20
40
0
60
(c)
1600
20
30
40
50
Time(hour)
(d)
ΔP = 34.9 kPa ΔP = 42.1 kPa
1400
2000
ΔP = 2.84 kPa
1600
1200 1000
dP = 25.6 Pa/h dt ΔP = 42.1 kPa
800 600 400
dP = 21.2 Pa/h dt ΔP =34.9 kPa
200
Pressure(Pa)
Pressure(Pa)
10
Time(hour)
1200
dP = 2673 Pa/h dt ΔP = 2.84 kPa
800
400
0
0 0
20
40
60
0.0
0.2
0.4
0.6
Time(hour)
Time(hour)
Fig. 9. Pressure increase rates for (a) N2, (b) O2, (c) CO2 and (d) H2O through the Al-metallized film.
Table 3 Gas permeabilities of O2, N2, CO2 and H2O through the Al-metallized film at 23 °C. Gases
DP
K 1015 [cc(gas@STP) cm(thickness)/cm2(area) s Pa (DP)] PET film (average value from Refs. [15–20])
Al-metallized film (measured value)
N2
27.5 kPa 92.2 kPa
0.549
0.0201 (±0.00143) 0.0188 (±0.00134)
O2
27.8 kPa 96.5 kPa
2.61
0.103 (±0.00733) 0.120 (±0.00849)
CO2
34.9 kPa 42.1 kPa
9.90
0.387 (±0.0275) 0.388 (±0.0275)
H2O
2.84 kPa
11,300
538 (±35.2)
4.2. Multiple layers of Al-coating It is clear that single coating is not practically useful for VIPs. If multiple layers of Al-coating are employed as shown in Fig. 12, the permeation rate is reduced significantly. This configuration is very useful and deserves further investigation. If both sides of the base film are Al-metallized as shown in Fig. 12(a), it is very unlikely that upper and lower pin-holes are aligned. Therefore, the effective gas permeability is expected to be significantly lower. The permeation rate can be again predicted using numerical computation.
Fig. 10. Distribution of pin-holes in the Al-metallized film by an optical microscope.
Considering computational capability, ten pin-holes are randomly distributed in each of the upper and the lower layers as shown in Fig. 13. Their coordinates are decided by random number as
x ¼ LRx ;
y ¼ LRy ;
ð15Þ
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is a dimensionless thickness of base film. In most cases, /1 is much smaller than 1. When /2 is very large, the film behaves like a semi-infinite medium [25]. This situation is similar to Eq. (14) with S in Eq. (13), so that
b1 ¼ Ndd ¼ /1 /2 ;
Fig. 11. Schematic diagram of permeation passage in the Al-metallized film.
where Rx and Ry are the random numbers lying between 0 and 1. Side walls are in adiabatic boundary condition. Parameters of pinholes from the tested film are used in this calculation. Twenty cases are calculated and the maximum and minimum results are 0.0173KPET and 0.0154KPET, respectively. They are averaged as 0.0162KPET with a standard deviation 0.0008KPET. The effective gas permeability is remarkably decreased compared with the earlier single-side Al-metallized film. For this case, the ratio b of mass fluxes of the pure base film and the both sides Al-metallized film is also investigated numerically.
b¼
K real ; K PET
ð16Þ
where Kreal is the permeability through double-side Al-metallized film. It is a function of the diameter, the distribution of pin-holes and thickness of the base film. They are nondimensionalized by the Buckingham p theorem as [26]
2 d b ¼ f Nd ; ¼ f ð/1 ; /2 Þ; d
2
/1 ¼ Nd ;
d /2 ¼ ; d
ð17Þ
where N [ea/m2] is the number distribution of pin-holes. The dimensionless variable /1 is an area fraction of pin-holes and /2
ð18Þ
This is also confirmed by numerical calculations. The effects of pinhole locations are investigated as shown in Fig. 14 and their results are summarized in Table 4. For smaller /1 and bigger /2, the numerical result approaches this theoretical limit. The effects of mis-alignment and multiple pin-holes are less than a few percent when /1 = 0.0001. Therefore, their effects can be neglected when /1 1 and /2 1. On the other hand, when the dimensionless thickness of base film /2 is very small, it can be treated as two-dimensional diffusion between small disks. This case is simplified as shown in Fig. 15 assuming a uniform distribution of pin-holes. This is approximated pffiffiffiffiffiffiffiffiffiffi by concentric diffusion with equivalent radius 1= 2pN [27]. The ratio b becomes then b2 as
b2 ¼
pNd2
ln
qffiffiffi 2
1
p2
2
p/1 /22
¼
ln Nd
ln
qffiffiffi 2
1
p2
:
ð19Þ
ln /1
However, this approximation needs a correction factor due to the ‘‘concentric diffusion’’ simplification. For intermediate values of /2, the ratio b may be expressed by a combination of b1 and b2. Therefore, correlation for this case is developed through numerous numerical simulations. Forty cases of ratios of mass fluxes are calculated with /1 = 0.01, 0.005, 0.003, 0.001 and /2 = 0.1, 0.3, 0.5, 1.0, 3.0, 5.0, 10, 30, 50, 100, respectively. Ten pin-holes on each layer are also considered as
Fig. 12. Schematic diagram of multiple layers of Al-coating.
Fig. 13. Schematic diagram for calculation of the effective gas permeability with both sides of Al-coating and randomly distributed pin-holes.
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(a) a pair of aligned pin-holes
(b) a pair of mis-aligned pin-holes
(c) two pairs of aligned pin-holes
(d) ten pairs of randomly distributed pin-holes
Fig. 14. Schematic diagram for numerical investigation of effects of mis-alignment of pin-holes.
Table 4 The effects of mis-alignment of pin-holes in Fig. 12. Pin-hole(s) arrangement
(a) A pair, aligned (b) A pair, misaligned (c) Two pairs, aligned (d) Ten pairs, randomlydistributed
b /1 = 0.001, /2 = 100
/1 = 0.0001, /2 = 100
Theoretical analysis
Numerical analysis
Theoretical analysis
Numerical analysis
0.1 0.1
0.0940 0.0923
0.01 0.01
0.00995 0.00987
0.1
0.0935
0.01
0.00992
0.1
0.0924
0.01
0.00972
2
3 n o /2 p / 6 7 qffiffiffi 2 b ¼ /1 /2 4 þ 1:97 tan1 ð/2 e0:0201/2 Þ 5: 10000/1 þ /2 2 ln 2 1 ln/ p
2
1
ð21Þ
before and their results are summarized in Table 5. The correlation for the ratio of mass fluxes is proposed as
b ¼ F 1 b1 þ aF 2 b2 ;
where a is the correction factor of b2, F1 and F2 are weighting factors of b1 and b2 respectively. Factor F1 increases from 0 to 1 and F2 decays from 1 to 0 with increasing /2, because b converges to ab2 with decreasing /2 and it converges to b1 with increasing /2 as mentioned before. It is confirmed, from the 40 numerical results, that F1 is a function of /1 and /2 and F2 is a function of /2 only. Finally, we propose the following correlation,
ð20Þ
To check the validity, the earlier test case of Fig. 13 (/1 = 0.00962, /2 = 1.85) is calculated as b = 0.0152 by this correlation. This is close to the numerical prediction b = 0.0162. More tests show that this correlation is reliable within 10% error. For further improvement, more than two Al-layers may be employed as shown in Fig. 12(b). In this case, each pair of neighboring Al-layers may be considered as a serially-connected diffusion resis-
Fig. 15. Simplification of diffusion between upper and lower pin-holes when /2 1.
21.7 12.7 3.42 +3.19 +6.44 +1.84 4.90 16.1 16.2 7.28 9.97 106 7.89 105 1.92 104 5.64 104 2.36 103 4.40 103 9.98 103 3.25 102 5.28 102 9.91 102 13.8 3.75 +1.19 +8.97 +14.0 +13.0 +11.3 0.493 5.11 +3.88 3.34 105 2.63 104 6.33 104 1.81 103 6.86 103 1.20 102 2.55 102 8.12 102 1.34 101 2.60 101
8.19 106 7.00 105 1.86 104 5.83 104 2.53 103 4.48 103 9.51 103 2.80 102 4.55 102 9.24 102
Relative error (%) Correlation Numerical simulation Relative error (%) Correlation
0.001
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445
tance. Therefore, a three Al-layers film can be treated as two double-side-coated films. More specially, when these are M + 1 coating layers (thus M PET layers between them), the permeation rate is reduced inversely proportional to M. In conclusion, more than two Al-layers have to be employed to efficiently block the gas permeation. 5. Conclusion An experimental apparatus is invented to measure the gas permeabilities through the Al-metallized film. Its reliability is proved by comparing the measurements with some known gas permeabilities through PET films. Gas permeabilities through the Al-metallized film are measured for a 12 lm PET film coated with a 33 nm Aluminum layer. Gas permeabilities for nitrogen, oxygen, carbon dioxide and water vapor are measured to be about 0.041KPET; only about 4.1% of those through uncoated PET film. Since it is still higher than those of metal sheets, resulting from the pin-holes, the effects of pin-holes are further investigated numerically. Through extensive computations for PET film with both side coatings, a correlation for the ratio of permeation rates between pure base film and both-side Al-metallized film is proposed as a function of diameter, area fraction of pin-holes and thickness of the base film. Multiple coating layers are shown to reduce the gas permeation significantly.
2.94 105 2.53 104 6.41 104 1.99 103 7.97 103 1.38 102 2.88 102 8.08 102 1.28 101 2.71 101 12.1 2.30 +1.51 +5.47 +11.3 +12.1 +10.8 +4.26 +0.133 14.3 6.08 105 4.76 104 1.15 103 3.25 103 1.20 102 2.05 102 4.15 102 1.23 101 1.99 101 3.88 101 0.1 0.3 0.5 1.0 3.0 5.0 10 30 50 100
10.7 2.30 0.737 +4.17 +4.16 +4.39 +7.04 +4.54 +7.11 12.0 1.41 104 1.10 103 2.64 103 7.45 103 2.68 102 4.48 102 8.65 102 2.25 101 3.40 101 6.27 101 1.27 104 1.08 103 2.62 103 7.78 103 2.80 102 4.69 102 9.31 102 2.36 101 3.66 101 5.60 101
5.42 105 4.66 104 1.16 103 3.44 103 1.35 102 2.33 102 4.65 102 1.28 101 2.00 101 3.39 101
0.003
Numerical simulation
0.005
Numerical simulation Numerical simulation
Relative error (%) Correlation 0.01
/1 /2
Table 5 Kreal/KPET for both side Al-metallized film by numerical simulation and correlation.
Correlation
Relative error (%)
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