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Method for determination of parameters for moisture simulations in photovoltaic modules and laminated glass
Solar Energy Materials & Solar Cells 144 (2016) 23–28
Contents lists available at ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Method for determination of parameters for moisture simulations in photovoltaic modules and laminated glass Rico Meitzner, Stefan-H. Schulze n Fraunhofer CSP, Otto-Eißfeldt-Straße 12, 06120 Halle (Saale), Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 27 July 2015 Accepted 17 August 2015
Moisture ingress into photovoltaic modules can be detrimental to the expected lifetime of the photovoltaic device. Hence, better understanding of this process and ways to predict the lifetime of a module are of high importance. Moisture ingress occurs through the polymeric materials used in a PV module, especially through the encapsulant which contacts all the sensitive parts in the module. In this work material parameters of polyvinyl butyral, an encapsulant mostly used for glass–glass modules, are presented and an examination of its lateral moisture transport and uptake behavior was undertaken to attain parameters for use in simulations. The uptake of moisture followed Fickian behavior. The absorption isotherm found was of Type III according to the classification by Brunauer, Emmett and Teller. & 2015 Published by Elsevier B.V.
Keywords: Photovoltaics Moisture Polyvinyl butyral Modeling
1. Introduction Sustainable energy production is one of the biggest problems humankind is facing today. As a steadily growing sector on the energy market and as a sustainable source of energy, solar energy production is getting more and more important. Photovoltaic modules are supposed to have a long lifetime of up to 25 years, while exposed to sometimes harsh environmental conditions. Factors which can lead to reduction in the efficiency of a module are temperature, thermomechanical stresses possibly producing cell breakage, wind load, snow and other sources and finally moisture, which can induce several failure modes like corrosion or delamination [1–3]. This work is focusing on the process of lateral moisture ingress into laminated glass–glass modules. A very important, but until today still very weakly probed, market for PV is building integrated photovoltaics (BIPV). This market has still large potential to grow in the coming years. Common module setups for BIPV are glass–glass modules with a polyvinyl butyral (PVB) interlayer as an encapsulant for the solar cells [4]. Generally, moisture ingresses into a PV module occurs through the polymeric components, the encapsulant or polymeric backsheet [5]. The process of water diffusion in encapsulation materials used in the PV sector was found to correspond very well with Fickian laws [5–10]. The quality of encapsulants as moisture barrier is mostly determined by measurement of their water vapor transmission rate (WVTR) [5,7–10]. A different approach was taken n
Corresponding author. Tel.: þ 49 345 5589 5510.
http://dx.doi.org/10.1016/j.solmat.2015.08.014 0927-0248/& 2015 Published by Elsevier B.V.
in [6] where a Ca-film deposited on glass was used to determine the depth of moisture ingression into a laminated sample made up of glass-encapsulant-glass. Moisture uptake capability of the polymer was determined either by immersion in water [11] or deduced from WVTR measurements [12,13,5,7–10]. The moisture uptake and permeation behavior of polyvinyl butyral were studied in this work. It was one of the first encapsulants used by the PV industry [11]. Polyvinyl butyral was later replaced by most manufacturers using ethylene vinylacetate. Polyvinyl butyral is a thermoplastic material and shows a strong adhesion to glass due to the high amount of hydroxl groups. These hydrophilic groups also lead to a relatively high moisture uptake [11,8,6]. In this work different approaches are taken to attain the moisture uptake behavior of PVB. Various methods to attain parameters such as the solubility of moisture and the diffusion coefficient were used. Those methods were Karl-Fischer-Titration in combination with a climate chamber, to carry out absorption experiments with PVB and obtain its diffusion coefficient and the equilibrium moisture absorption. Also measurements of the water vapor transmission rate (WVTR) were performed using a MOCON water permeation measurement device. From those measurements the temperature dependence of the diffusion coefficient was determined. These parameters obtained can be used to create a numerical simulation of the moisture uptake and distribution in a PV module from meteorological data. These data regularly contain the outdoor temperature, the relative humidity, wind speeds and precipitation. From this information combined with moisture uptake and distribution behavior of the components PV module simulations can be performed.
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2. Theory The process of moisture uptake and transport in a photovoltaic module can proceed along several ways, depending on the explicit design of the module. Inorganic components of a module like the connectors, the solar cells or glass are generally impenetrable for water [5]. Thus, only the polymeric components have to be taken into consideration for the moisture uptake and transport process. In a glass–glass module water can only penetrate through the edges where the encapsulant is exposed to the environment. At this face the polymer absorbs moisture from its surrounding. The moisture at this surface, which can be expected to be in equilibrium with the air instantaneously, will then penetrate the encapsulant following the concentration gradient. But it can permeate not only through the polymer, but also along the interface between the polymer and the glass, the solar cells and the connectors [2]. Depending on the exact strength of the bonding between the glass and the encapsulant also moisture transport along the interface can occur. Moisture in a PV module is laterally absorbed at the edges for a glass–glass-module and then diffuses through the encapsulant further into the module. In the scope of this work Ficks laws are applied to describe the diffusion of moisture in the polymer. They are Ficks first,
J = − D∇C,
(1)
and second law,
∂C = ∇(D∇C ), ∂t
(2)
where J is the diffusive flux, D the diffusion coefficient, ∇C the concentration gradient. In Eq. (2) C represents the concentration and t the time elapsed during diffusion [13]. The initial conditions applied to solve these equations were
C (x = l) = C0,
C (x = 0) = 0.
(3)
Absorption of moisture in polymers follows Henry's law,
a eq = KH ·Ceq,
(4)
Volume fraction of sorbed penetrant
with aeq being the equilibrium concentration in the material of interest, KH the Henry-coefficient giving the solubility, and Ceq the equilibrium concentration of the penetrant. Henry's law generally applies to hydrophobic polymers above glass transition temperature [12,13]. Brunauer, Emmett and Teller (BET) classified absorption isotherms into 5 different classes. The 5 types of absorption isotherms are depicted in a principal way in Fig. 1. Type I is a Langmuir isotherm which applies to microporous solids, Types II and III describe adsorption to macroporous or non-porous solids and Types IV and V are applicable to microporous or meso-porous solids [14] (Fig. 2).
I
II
III
IV
V
Henry's Law
Fig. 2. Chemical formulation of PVB [21].
Further, they developed a model for absorption based on the model by Langmuir.
a 1 c −1 = + ( BET )a ϕ (1 − a) ϕm cBET ϕm cBET
(5)
is the formula postulated by BET. With ϕ being the volume fraction of penetrant, ϕm the volume fraction of a complete penetrant monolayer, a the activity of the penetrant. And cBET is a parameter of the BET model. The model generally describes moisture sorption in glassy polymers for activities from 0 to 0.5 very well [14]. There are also dissolution theories like the Flory–Huggins theory which assumes a weak interaction between penetrant and polymer and deviations from ideal assumptions are accounted by incompatibility of their molecule sizes. This theory was further developed by Perrin and Favre, where a parameter which accounts for interacting penetrant molecules was added leading to the following formulation:
ϕ=
e (k s − k p ) a − 1 , (ks − kp )/kp
(6)
where ks is a parameter which shall describe the interaction between penetrant molecules and kp the interaction between polymer and penetrant [14]. For Type III isotherm this mode showed a good agreement over the whole activity range [14]. This model is also called the ENSIC model [14]. Temperature also has an important impact on moisture transport behavior in polymers, the dependence of the diffusion process can thereby be described with an Arrhenius equation.
D = Da ·exp (
ED ), RT
(7)
with Da giving a pre-exponential factor, ED the activation energy for diffusion, R the universal gas constant and T the absolute temperature [15]. The increase of diffusivity with temperature can be explained by the free-volume theory. Free-volume theory postulates that a certain amount of the volume, which depends on the individual polymer, is not occupied by the macromolecular chains due to packing issues. Hence this non-occupied volume is available for diffusion processes. Although not all voids are necessarily large enough to allow for a pathway for a diffusing molecule. The movement of chains can rearrange free-volume and thereby create new paths large enough for diffusion. At higher temperatures the movement of the chains is more easily possible and the diffusion coefficient increases with temperature [16].
3. Methods and materials 3.1. Materials
relative pressure Fig. 1. Sorption isotherm classification of Brunauer, Emmett and Teller, also a linear isotherm according to Henry's law. The sorbed volume fraction is plotted as a function of relative pressure [14].
Polyvinyl butyral is an amorphous thermoplastic polymer. It is made from polyvinyl alcohol by condensation with n-butyraldehyde, while the polyvinyl alcohol is made from polyvinyl acetate. Hence, PVB contains a certain percentage of vinyl alcohol
R. Meitzner, S.-H. Schulze / Solar Energy Materials & Solar Cells 144 (2016) 23–28
and vinyl acetate groups and the hydroxyl groups of the polyvinyl alcohol allow for a good adhesion towards glass by hydrogen bonding. The glass transition temperature of PVB is 19 ± 5 °C [17,18]. The PVB used in this work was Trosifol R40 from Kuraray. Polyvinyl butyral is classified as a hydrophilic material. Other hydrophilic materials show a dependence of their diffusion coefficient on the concentration. Although this dependence cannot be easily predicted as to weather it is positive, i.e. the diffusion coefficient increases with hydrophilic behavior of the polymer, or if it is negative. It is further known that PVB shows a Type III isotherm, hence Henry's law cannot be applied [19]. 3.2. Methods In Fig. 3 a summary of the necessary procedures to obtain the parameters mentioned in the theory section is depicted. For the procedures in all strands polyvinyl buytral films of 0.76 mm thickness were cut in 20 by 30 cm sized sheets. These were laminated by vacuum lamination at 150 °C and a pressure of 1000 mbar was applied for 18 min. After lamination, the film thickness was 0.737 mm on average. Further material properties are contained in Table 1. For the first strand in Fig. 3 the samples were exposed to different environmental conditions in a climate chamber. In 20 min intervals for the first 6 h and afterwards once every 24 h, samples have been taken for an overall duration of 72 h. Their mass uptake was determined by Karl-Fischer-Titration. And from these results their diffusion coefficient was calculated. The temperature thereby was 25 °C and the relative humidity 50%, 65%, 75%, 85%, 95%. Those experiments were performed to obtain the diffusion coefficient D according to Eqs. (1) and (2). Following the procedures in the second strand of Fig. 3, WVTR measurements using a MOCON PERMATRAN W 3/33 MG Plus were performed at different temperatures. A constant relative humidity of 100% on the feed side has been set to obtain the activation energy for the moisture diffusion. Slightly modified equations as Köhl et al. [7] presented them were used to determine the diffusion coefficient for the thermal activation of the material. Köhl et al. used the concentration as gradient for their formula. We instead decided to use the relative humidity as gradient between both sides of the foil. This was done because the relative humidity can be measured directly and it is the data given in meteorological data sets. Furthermore this modification is justified because the temperature on both sides of the foil is equal. Hence the saturation Soaking at different temperatures and/or relative humidities
WVTR at different temperatures and/or relative humidites
Start: short intervalls at each r.H. End: Once a day
Soaking at different temperatures and/or relative humidities Measurement of moisture content at each r.H. after 3 d
Determination of D according to Eq. 7
Determination of D according to Köhl et al (2009)
Determination of D(C) by plotting D against C
Plot lnD against 1/T, calculate according to Eq. 6
Determination of coefficents for sorption with Eq. 3 and Eq. 5
25
Table 1 Material data of Trosifol R40 (PVB) [21]. Density
(g/cm3)
Thermal conductivity (W/m)
Specific resistance Specific heat (J/WK) (Ω cm)
1.065
0.2
2.0E12
1.85
pressure of moisture is the same. The formula is as follows:
jx =
DS (ϕfeed − ϕpurge ), lf
(8)
with jx representing the moisture flux across the foil, D the diffusion coefficient, S the solubility of water in the foil in relation to the moisture activity [7]. The thickness of the foil is given by lf, ϕfeed represents the relative humidity on the feed side and ϕpurge the relative humidity on the purge side. With these diffusion coefficients the activation energy of the moisture transport process can be calculated as given in Eq. (7). For the procedures summarized in the third strand further absorption experiments were performed at 85 °C and different relative humidity (5%, 10%, 15%, 20%, 35%, 40%, 45%, 50%, 55%, 60%, 80%, 85%, 90%, 95% r.H.). Through these tests the absorptivity of PVB was obtained. Samples were exposed at each humidity until they reached equilibrium, which took 2 days and was determined in earlier experiments. Samples were taken from the climate chamber, sealed in air-tight flasks and their weight determined. Their moisture content was then measured using Karl-FischerTitration. From these measurements the parameters of Eqs. (4), (5) and (6) have been determined. Karl-Fischer-Titration as used is an electrochemical method to determine the moisture content in a sample. The titrator used was a METTLER TOLEDO C30. The moisture was extracted in an oven at 160 °C for 20 min. The chemical reaction used in Karl-FischerTitration is highly specific to water, hence the method will not be perturbed by other volatile components eventually contained in the foil, which could have also been evaporated at higher temperatures [20]. Additionally, simulations based on finite element method (FEM) were performed with the experimentally determined coefficients. The applied boundary conditions were chosen according to Henry's law or the ENSIC model at 50% and 100% r.H. A digital 2D model of a glass–glass-laminate was created, calculations have been carried out using the FEM software ANSYS. The model consisted of a square with an edge length of 5 cm. The mesh size was set to 1 mm for the whole model. The boundary conditions were set in a way that two neighboring edges had a set diffusion flow of 0 while on the other two neighboring edges the boundary conditions itself were applied. The top and bottom faces had no flow of moisture as well. The results of the simulation were analyzed along the diagonal from the corner, where the two neighboring edges to which the boundary conditions were applied collided, to the corner where the two neighboring face with zero flow collided. So the basic idea behind the simulation was an absorption experiment with a 10 cm by 10 cm laminated glass specimen containing PVB layer, exposed at a constant atmosphere.
4. Results and discussion Material Parameters for use in simulations Fig. 3. Procedure to determine material parameters for simulations of moisture ingress into a PV module.
The results of the absorption experiments at 25 °C and 95% r.H. are given in Fig. 4. They show a good agreement with Fickian absorption, according to Eqs. (9) and (10)
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Mt 8 = 1 − 2 b, π M∞
∞
b=
∑ m=0
π 2t 1 exp [−D (2m + 1)2 2 ], 2 (2m + 1) l
(9)
(10)
with Mt being the instantaneous mass of absorbed moisture, M∞ the mass of absorbed moisture at equilibrium concentration, l the thickness of the foil and t the passed time [13]. The diffusion coefficient was determined to be D = 6.31 × 10−8 cm2/s. In Fig. 5 the results from WVTR measurements at different temperatures are depicted. The results show a good agreement with the assumption of an Arrhenius-like behavior of the thermal activation of moisture diffusion in PVB. The increase of the diffusion coefficient at higher temperatures results from the increase of the kinetic energy of the polymer chains. Hence, they are easier capable of giving way for diffusing molecules, which allows for more possible paths for molecules of water to move through the network [12,15]. Further, with increasing temperature the hole free-volume of the polymer increases, thus there are also more possible paths for a penetrant molecule to find a way through the polymer [14,16]. In Fig. 6 the absorption isotherm at 85 °C for the studied PVB and the fit according to the ENSIC model is depicted. As expected it shows a Type III isotherm [19]. The sum of squares for the fit was 0.27602. Also, as seen in Fig. 7, Henry's law was fitted with the assumption of 0% moisture content at 0% r.H. and the determined moisture content at 95% r.H. in accordance with the procedure in other publications [6]. The sum of squares for the resulting fit was 12.81 hence it was 2 orders of magnitude worse than the fit according to the ENSIC model. The largest deviation between Henry's law and the experimentally determined values were at a ¼0.5 with a difference of 1.41% moisture content by weight. A basic assumption for Henry's law is an ideal solution, which means no interaction between the matrix and the molecules solved and no interaction between the solved molecules is assumed. This assumption does not hold for PVB, thus the deviation of the experimental data from Henry's law can be explained. Polyvinyl butyral is a highly polar material. Due to its molecular structure, there are many available sites for water molecules to form hydrogen bonds with. Especially at higher activities water molecules can also start to interact with each other. The ratio between ks and kp, see Table 2, gives a hint that interaction of water molecules with the PVB seems to be more important than the interaction between water molecules themselves [14].
Fig. 5. Temperature dependence of the diffusion coefficient D, measured at 25 °C, 35 °C, 45 °C and 50 °C, D was determined according to the method used by Köhl et al. [7].
Fig. 6. Fit according to ENSIC model, see Eq. (6).
Fig. 7. Linear fit in accordance with Henry's law to the absorption data from the experiment, Eq. (4) was used to fit the data.
Table 2 Experimentally obtained material parameters for diffusion and absorption for PVB.
Da exp (
Fig. 4. Experimental results for the absorption experiment at 95% r.H.
ED ) RT
Da = 8.65·10−4 m2/s ED ¼ 19.19 J/mol K
aeq = KH ·Ceq KH = 4.65
ϕ=
e(ks − kp ) a − 1 (ks − kp ) / kp
kp = 3.61
ks = 0.96029
R. Meitzner, S.-H. Schulze / Solar Energy Materials & Solar Cells 144 (2016) 23–28
27
A
100,00 mm
100,00 mm
Fig. 8. Area marked by the dotted line represents the FEM model as described in the methods part. Data were extracted along path A.
Fig. 9. Simulation results for constant diffusion coefficient and boundary conditions according to the assumption of Henry's law, each curve represents the moisture distribution over time at a certain depth within the sample. With the topmost curve being furthest to the edge and the lowest being the innermost spot.
Fig. 8 shows along which path the following data was extracted from the simulation of the laminates. Path A starts in the corner, which is defined as x ¼0, and ends in the middle of the laminate. In Fig. 9 the results for the simulation at 50% r.H. with boundary conditions according to Henry's law are shown. Even after 8000 h the equilibrium was not yet reached in the center of the sample. Fig. 10 shows the results of the simulation with boundary conditions according to the ENSIC model at 50% r.H. After 8000 h the equilibrium in the center was not yet reached. Both results were compared as shown in Fig. 11. The graph plotted depicts the ratio between both according to
(ωHenry − ωENSIC )/ωHenry,
Fig. 10. Simulation results for constant diffusion coefficient and boundary conditions according to the assumption of ENSIC model, each curve represents the moisture distribution over time at a certain depth in mm within the sample. With the topmost curve being furthest to the edge and the lowest being the innermost spot.
Fig. 11. Comparison of the simulation results for constant diffusion coefficient and boundary conditions according to the assumption of Henry's law and the ENSIC model, each curve represents the relative difference over time at a certain depth in mm within the sample. The arrow indicates which curve is furthest outside, with curves towards the end of the arrow are closer to the middle of the sample.
at this point is 3.2·105% with a moisture content of 1E-8 with Henry's law and 3.217E-5 with the ENSIC model. According to Eqs. (1) and (2) one would expect that the laminate with the higher gradient, which is the one with boundary conditions according to Henry's law, reaches equilibrium faster. But the simulation showed that the equilibrium is reached faster with the boundary conditions according to the ENSIC model, representing the model with the smaller gradient.
(11)
with ωHenry being the moisture content from the simulation with Henry's law and ωENSIC being the moisture content from the simulation with the ENSIC model. On one hand there is the difference between both models when they both have reached equilibrium. There is a resulting difference in moisture content between both models at equilibrium of 1.41% moisture by weight, both results differ by this value close to the perimeter where equilibrium is obtained within 8000 h. Additional comparison of the simulations shows when approaching 1000 h the moisture content in the laminate with boundary conditions according to the ENSIC model becomes higher than in the laminate simulation according to Henry's law. This difference becomes higher when coming closer to the center of the laminate (Figs. 8 and 11). This difference reaches its maximum at 1060 h for the results at a depth of 70 mm. The difference
5. Conclusions The standard method to determine the moisture uptake for a polymer in the PV research literature is to calculate the sorptivity from permeation experiments at 100% r.H. This only allows for the application of Henry's Law, but as we could see this does not necessarily hold for every polymer used in the PV sector. And although on first sight it appears that Henry's Law is a viable option for a worst case scenario. The simulations showed that it does not in every case deliver the highest moisture content for a given depth and time. At an ingression depth of 20mm up to the center for a glass– glass-laminate of 100 mm by 100 mm the moisture concentration actually is higher with the lower boundary conditions at 50% r.H. While the lower boundary conditions are connected to the usage of the ENSIC model in this case. When this ratio is scaled up to
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larger areas specimens this would mean that from 25% of the way from the corner to the center the moisture content is higher than expected from the approach with Henry's law. When taking into consideration the low tolerance against moisture for certain coming PV technologies and also for thin-film PV in general, this can have a huge impact in the predictability of simulations. When performing simulations with climate data that have constant intermediate relative humidity, this means between 30% r.H. and 70% r.H., for timescales of 500 h and 2000 h. As is the case for the humid continental climates for example. For arid or tropical climates in contrast the difference would not be so important because they have a constant high or low humidity an equilibrium would be reached where Henry's law and the ENSIC model are nearly in agreement, see Fig. 7.
Acknowledgments Gratefully acknowledged is the funding of the project S-PAC, grant number 03WKBW05C, by German Ministry for Education and research BMBF.
References [1] G. Mon, L. Wen, J.R. Ross, Encapsulant free-surfaces and interfaces: critical parameters in controlling cell corrosion, in: 19th IEEE Photovoltaic Specialists Conference, 1987. [2] G. Mon, L. Wen, J.R. Ross, Water-module interaction studies, in: 1988 Photovoltaic Specialists Conference, Conference Record of the Twentieth IEEE, 1988. [3] G. Mon, L. Wen, R. Sugimura, Jr., Reliability studies of photovoltaic module insulation systems, in: Proceedings of the 19th Electrical Electronics Insulation Conference, 1989, Chicago '89 EEIC/ICWA Exposition, 1989. [4] F. Azadian, M. Radzi, A general approach toward building integrated photovoltaic systems and its implementation barriers: a review, Renew. Sustain. Energy Rev. 22 (2013) 527–538. [5] M.D. Kempe, Modeling of rates of moisture ingress into photovoltaic modules, Sol. Energy Mater. Sol. Cells 90 (2006) 2720–2738.
[6] M.D. Kempe, A.A. Dameron, M.O. Reese, Evaluation of moisture ingress from the perimeter of photovoltaic modules, Progress in Photovoltaics: Research and Applications 22 (11) (2014) 1159–1171. [7] M. Köhl, O. Angeles-Palacios, D. Philipp, K.-A. Weiß, Polymer films in photovoltaic modules: Analysis and modeling of permeation processes, in: J. W. Martin, R.A. Ryntz, J. Chin, R. Dickie (Eds.), Service Life Prediction of Polymeric Materials: Global Perspectives, Springer Verlag, 2009, pp. 361–371. [8] M. Köhl, M. Heck, S. Wiesmeier, Modelling of conditions for accelerated lifetime testing of humidity impact on PV-modules based on monitoring of climatic data, Sol. Energy Mater. Sol. Cells 99 (2012) 282–291. [9] N. Kim, C. Han, Laehoon Lee, D. Baek, D. Kim, Determination of moisture ingress through various encapsulants used in CIGS PV module under continuously varying environment, in: 2012 38th IEEE of Photovoltaic Specialists Conference (PVSC), 2012. [10] N. Kim, C. Han, Experimental characterization and simulation of water vapor diffusion through various encapsulants used in PV modules, Sol. Energy Mater. Sol. Cells 116 (2013) 68–75. [11] S.A. Sala, M. Campaniello, A. Bailini, Experimental study of polymers as encapsulating materials for photovoltaic modules, in: Microelectronics and Packaging Conference, 2009, pp. 1–7. [12] J. Crank, G. Park, Diffusion in Polymers, Academic Press, 1968 (Published in: Microelectronics and Packaging Conference, EMPC 15–18 June 2009, pp. 1–7, E-ISBN : 978-0-6152-9868-9; Print ISBN: 978-1-4244-4722-0; INSPEC Accession Number: 10893493). [13] J. Crank, The Mathematics of Diffusion, Oxford University Press, 1975. [14] G. van der Wel, O. Adan, Moisture in organic coatings—a review, Prog. Org. Coat. 37 (November (1–2)) (1999) 1–14. [15] W.W. Brandt, Model calculation of the temperature dependence of small molecule diffusion in high polymers, J. Phys. Chem. 63 (1959) 1080–1085. [16] J.S. Vrentas, A free-volume interaction of the influence of the glass transition on diffusion in amorphous polymers, J. Appl. Polym. Sci. 22 (1978) 2325–2339. [17] D.C. Miller, M.D. Kempe, S.H. Glick, S.R. Kurtz, Creep in photovoltaic modules: examining the stability of polymeric materials and components, in: 2010 35th IEEE of Photovoltaic Specialists Conference (PVSC), 2010. [18] A. Dhaliwal, J. Hay, The characterization of polyvinyl butyral by thermal analysis, Thermochim. Acta 391 (2002) 245–255. [19] P.M. Hauser, D. McLaren, Permeation through and sorption of water vapor by high polymers, Ind. Eng. Chem. Res. 40 (1) (1948) 112–117. [20] A. Stark, P. Behrend, O. Braun, A. Müller, J. Ranke, B. Ondruschkaa, B. Jastorff, Purity specification methods for ionic liquids, Green Chem. 10 (2008) 1152–1161. [21] Trosifol R40 data sheet, 2013.
Contents lists available at ScienceDirect
Solar Energy Materials & Solar Cells journal homepage: www.elsevier.com/locate/solmat
Method for determination of parameters for moisture simulations in photovoltaic modules and laminated glass Rico Meitzner, Stefan-H. Schulze n Fraunhofer CSP, Otto-Eißfeldt-Straße 12, 06120 Halle (Saale), Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 27 July 2015 Accepted 17 August 2015
Moisture ingress into photovoltaic modules can be detrimental to the expected lifetime of the photovoltaic device. Hence, better understanding of this process and ways to predict the lifetime of a module are of high importance. Moisture ingress occurs through the polymeric materials used in a PV module, especially through the encapsulant which contacts all the sensitive parts in the module. In this work material parameters of polyvinyl butyral, an encapsulant mostly used for glass–glass modules, are presented and an examination of its lateral moisture transport and uptake behavior was undertaken to attain parameters for use in simulations. The uptake of moisture followed Fickian behavior. The absorption isotherm found was of Type III according to the classification by Brunauer, Emmett and Teller. & 2015 Published by Elsevier B.V.
Keywords: Photovoltaics Moisture Polyvinyl butyral Modeling
1. Introduction Sustainable energy production is one of the biggest problems humankind is facing today. As a steadily growing sector on the energy market and as a sustainable source of energy, solar energy production is getting more and more important. Photovoltaic modules are supposed to have a long lifetime of up to 25 years, while exposed to sometimes harsh environmental conditions. Factors which can lead to reduction in the efficiency of a module are temperature, thermomechanical stresses possibly producing cell breakage, wind load, snow and other sources and finally moisture, which can induce several failure modes like corrosion or delamination [1–3]. This work is focusing on the process of lateral moisture ingress into laminated glass–glass modules. A very important, but until today still very weakly probed, market for PV is building integrated photovoltaics (BIPV). This market has still large potential to grow in the coming years. Common module setups for BIPV are glass–glass modules with a polyvinyl butyral (PVB) interlayer as an encapsulant for the solar cells [4]. Generally, moisture ingresses into a PV module occurs through the polymeric components, the encapsulant or polymeric backsheet [5]. The process of water diffusion in encapsulation materials used in the PV sector was found to correspond very well with Fickian laws [5–10]. The quality of encapsulants as moisture barrier is mostly determined by measurement of their water vapor transmission rate (WVTR) [5,7–10]. A different approach was taken n
Corresponding author. Tel.: þ 49 345 5589 5510.
http://dx.doi.org/10.1016/j.solmat.2015.08.014 0927-0248/& 2015 Published by Elsevier B.V.
in [6] where a Ca-film deposited on glass was used to determine the depth of moisture ingression into a laminated sample made up of glass-encapsulant-glass. Moisture uptake capability of the polymer was determined either by immersion in water [11] or deduced from WVTR measurements [12,13,5,7–10]. The moisture uptake and permeation behavior of polyvinyl butyral were studied in this work. It was one of the first encapsulants used by the PV industry [11]. Polyvinyl butyral was later replaced by most manufacturers using ethylene vinylacetate. Polyvinyl butyral is a thermoplastic material and shows a strong adhesion to glass due to the high amount of hydroxl groups. These hydrophilic groups also lead to a relatively high moisture uptake [11,8,6]. In this work different approaches are taken to attain the moisture uptake behavior of PVB. Various methods to attain parameters such as the solubility of moisture and the diffusion coefficient were used. Those methods were Karl-Fischer-Titration in combination with a climate chamber, to carry out absorption experiments with PVB and obtain its diffusion coefficient and the equilibrium moisture absorption. Also measurements of the water vapor transmission rate (WVTR) were performed using a MOCON water permeation measurement device. From those measurements the temperature dependence of the diffusion coefficient was determined. These parameters obtained can be used to create a numerical simulation of the moisture uptake and distribution in a PV module from meteorological data. These data regularly contain the outdoor temperature, the relative humidity, wind speeds and precipitation. From this information combined with moisture uptake and distribution behavior of the components PV module simulations can be performed.
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2. Theory The process of moisture uptake and transport in a photovoltaic module can proceed along several ways, depending on the explicit design of the module. Inorganic components of a module like the connectors, the solar cells or glass are generally impenetrable for water [5]. Thus, only the polymeric components have to be taken into consideration for the moisture uptake and transport process. In a glass–glass module water can only penetrate through the edges where the encapsulant is exposed to the environment. At this face the polymer absorbs moisture from its surrounding. The moisture at this surface, which can be expected to be in equilibrium with the air instantaneously, will then penetrate the encapsulant following the concentration gradient. But it can permeate not only through the polymer, but also along the interface between the polymer and the glass, the solar cells and the connectors [2]. Depending on the exact strength of the bonding between the glass and the encapsulant also moisture transport along the interface can occur. Moisture in a PV module is laterally absorbed at the edges for a glass–glass-module and then diffuses through the encapsulant further into the module. In the scope of this work Ficks laws are applied to describe the diffusion of moisture in the polymer. They are Ficks first,
J = − D∇C,
(1)
and second law,
∂C = ∇(D∇C ), ∂t
(2)
where J is the diffusive flux, D the diffusion coefficient, ∇C the concentration gradient. In Eq. (2) C represents the concentration and t the time elapsed during diffusion [13]. The initial conditions applied to solve these equations were
C (x = l) = C0,
C (x = 0) = 0.
(3)
Absorption of moisture in polymers follows Henry's law,
a eq = KH ·Ceq,
(4)
Volume fraction of sorbed penetrant
with aeq being the equilibrium concentration in the material of interest, KH the Henry-coefficient giving the solubility, and Ceq the equilibrium concentration of the penetrant. Henry's law generally applies to hydrophobic polymers above glass transition temperature [12,13]. Brunauer, Emmett and Teller (BET) classified absorption isotherms into 5 different classes. The 5 types of absorption isotherms are depicted in a principal way in Fig. 1. Type I is a Langmuir isotherm which applies to microporous solids, Types II and III describe adsorption to macroporous or non-porous solids and Types IV and V are applicable to microporous or meso-porous solids [14] (Fig. 2).
I
II
III
IV
V
Henry's Law
Fig. 2. Chemical formulation of PVB [21].
Further, they developed a model for absorption based on the model by Langmuir.
a 1 c −1 = + ( BET )a ϕ (1 − a) ϕm cBET ϕm cBET
(5)
is the formula postulated by BET. With ϕ being the volume fraction of penetrant, ϕm the volume fraction of a complete penetrant monolayer, a the activity of the penetrant. And cBET is a parameter of the BET model. The model generally describes moisture sorption in glassy polymers for activities from 0 to 0.5 very well [14]. There are also dissolution theories like the Flory–Huggins theory which assumes a weak interaction between penetrant and polymer and deviations from ideal assumptions are accounted by incompatibility of their molecule sizes. This theory was further developed by Perrin and Favre, where a parameter which accounts for interacting penetrant molecules was added leading to the following formulation:
ϕ=
e (k s − k p ) a − 1 , (ks − kp )/kp
(6)
where ks is a parameter which shall describe the interaction between penetrant molecules and kp the interaction between polymer and penetrant [14]. For Type III isotherm this mode showed a good agreement over the whole activity range [14]. This model is also called the ENSIC model [14]. Temperature also has an important impact on moisture transport behavior in polymers, the dependence of the diffusion process can thereby be described with an Arrhenius equation.
D = Da ·exp (
ED ), RT
(7)
with Da giving a pre-exponential factor, ED the activation energy for diffusion, R the universal gas constant and T the absolute temperature [15]. The increase of diffusivity with temperature can be explained by the free-volume theory. Free-volume theory postulates that a certain amount of the volume, which depends on the individual polymer, is not occupied by the macromolecular chains due to packing issues. Hence this non-occupied volume is available for diffusion processes. Although not all voids are necessarily large enough to allow for a pathway for a diffusing molecule. The movement of chains can rearrange free-volume and thereby create new paths large enough for diffusion. At higher temperatures the movement of the chains is more easily possible and the diffusion coefficient increases with temperature [16].
3. Methods and materials 3.1. Materials
relative pressure Fig. 1. Sorption isotherm classification of Brunauer, Emmett and Teller, also a linear isotherm according to Henry's law. The sorbed volume fraction is plotted as a function of relative pressure [14].
Polyvinyl butyral is an amorphous thermoplastic polymer. It is made from polyvinyl alcohol by condensation with n-butyraldehyde, while the polyvinyl alcohol is made from polyvinyl acetate. Hence, PVB contains a certain percentage of vinyl alcohol
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and vinyl acetate groups and the hydroxyl groups of the polyvinyl alcohol allow for a good adhesion towards glass by hydrogen bonding. The glass transition temperature of PVB is 19 ± 5 °C [17,18]. The PVB used in this work was Trosifol R40 from Kuraray. Polyvinyl butyral is classified as a hydrophilic material. Other hydrophilic materials show a dependence of their diffusion coefficient on the concentration. Although this dependence cannot be easily predicted as to weather it is positive, i.e. the diffusion coefficient increases with hydrophilic behavior of the polymer, or if it is negative. It is further known that PVB shows a Type III isotherm, hence Henry's law cannot be applied [19]. 3.2. Methods In Fig. 3 a summary of the necessary procedures to obtain the parameters mentioned in the theory section is depicted. For the procedures in all strands polyvinyl buytral films of 0.76 mm thickness were cut in 20 by 30 cm sized sheets. These were laminated by vacuum lamination at 150 °C and a pressure of 1000 mbar was applied for 18 min. After lamination, the film thickness was 0.737 mm on average. Further material properties are contained in Table 1. For the first strand in Fig. 3 the samples were exposed to different environmental conditions in a climate chamber. In 20 min intervals for the first 6 h and afterwards once every 24 h, samples have been taken for an overall duration of 72 h. Their mass uptake was determined by Karl-Fischer-Titration. And from these results their diffusion coefficient was calculated. The temperature thereby was 25 °C and the relative humidity 50%, 65%, 75%, 85%, 95%. Those experiments were performed to obtain the diffusion coefficient D according to Eqs. (1) and (2). Following the procedures in the second strand of Fig. 3, WVTR measurements using a MOCON PERMATRAN W 3/33 MG Plus were performed at different temperatures. A constant relative humidity of 100% on the feed side has been set to obtain the activation energy for the moisture diffusion. Slightly modified equations as Köhl et al. [7] presented them were used to determine the diffusion coefficient for the thermal activation of the material. Köhl et al. used the concentration as gradient for their formula. We instead decided to use the relative humidity as gradient between both sides of the foil. This was done because the relative humidity can be measured directly and it is the data given in meteorological data sets. Furthermore this modification is justified because the temperature on both sides of the foil is equal. Hence the saturation Soaking at different temperatures and/or relative humidities
WVTR at different temperatures and/or relative humidites
Start: short intervalls at each r.H. End: Once a day
Soaking at different temperatures and/or relative humidities Measurement of moisture content at each r.H. after 3 d
Determination of D according to Eq. 7
Determination of D according to Köhl et al (2009)
Determination of D(C) by plotting D against C
Plot lnD against 1/T, calculate according to Eq. 6
Determination of coefficents for sorption with Eq. 3 and Eq. 5
25
Table 1 Material data of Trosifol R40 (PVB) [21]. Density
(g/cm3)
Thermal conductivity (W/m)
Specific resistance Specific heat (J/WK) (Ω cm)
1.065
0.2
2.0E12
1.85
pressure of moisture is the same. The formula is as follows:
jx =
DS (ϕfeed − ϕpurge ), lf
(8)
with jx representing the moisture flux across the foil, D the diffusion coefficient, S the solubility of water in the foil in relation to the moisture activity [7]. The thickness of the foil is given by lf, ϕfeed represents the relative humidity on the feed side and ϕpurge the relative humidity on the purge side. With these diffusion coefficients the activation energy of the moisture transport process can be calculated as given in Eq. (7). For the procedures summarized in the third strand further absorption experiments were performed at 85 °C and different relative humidity (5%, 10%, 15%, 20%, 35%, 40%, 45%, 50%, 55%, 60%, 80%, 85%, 90%, 95% r.H.). Through these tests the absorptivity of PVB was obtained. Samples were exposed at each humidity until they reached equilibrium, which took 2 days and was determined in earlier experiments. Samples were taken from the climate chamber, sealed in air-tight flasks and their weight determined. Their moisture content was then measured using Karl-FischerTitration. From these measurements the parameters of Eqs. (4), (5) and (6) have been determined. Karl-Fischer-Titration as used is an electrochemical method to determine the moisture content in a sample. The titrator used was a METTLER TOLEDO C30. The moisture was extracted in an oven at 160 °C for 20 min. The chemical reaction used in Karl-FischerTitration is highly specific to water, hence the method will not be perturbed by other volatile components eventually contained in the foil, which could have also been evaporated at higher temperatures [20]. Additionally, simulations based on finite element method (FEM) were performed with the experimentally determined coefficients. The applied boundary conditions were chosen according to Henry's law or the ENSIC model at 50% and 100% r.H. A digital 2D model of a glass–glass-laminate was created, calculations have been carried out using the FEM software ANSYS. The model consisted of a square with an edge length of 5 cm. The mesh size was set to 1 mm for the whole model. The boundary conditions were set in a way that two neighboring edges had a set diffusion flow of 0 while on the other two neighboring edges the boundary conditions itself were applied. The top and bottom faces had no flow of moisture as well. The results of the simulation were analyzed along the diagonal from the corner, where the two neighboring edges to which the boundary conditions were applied collided, to the corner where the two neighboring face with zero flow collided. So the basic idea behind the simulation was an absorption experiment with a 10 cm by 10 cm laminated glass specimen containing PVB layer, exposed at a constant atmosphere.
4. Results and discussion Material Parameters for use in simulations Fig. 3. Procedure to determine material parameters for simulations of moisture ingress into a PV module.
The results of the absorption experiments at 25 °C and 95% r.H. are given in Fig. 4. They show a good agreement with Fickian absorption, according to Eqs. (9) and (10)
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Mt 8 = 1 − 2 b, π M∞
∞
b=
∑ m=0
π 2t 1 exp [−D (2m + 1)2 2 ], 2 (2m + 1) l
(9)
(10)
with Mt being the instantaneous mass of absorbed moisture, M∞ the mass of absorbed moisture at equilibrium concentration, l the thickness of the foil and t the passed time [13]. The diffusion coefficient was determined to be D = 6.31 × 10−8 cm2/s. In Fig. 5 the results from WVTR measurements at different temperatures are depicted. The results show a good agreement with the assumption of an Arrhenius-like behavior of the thermal activation of moisture diffusion in PVB. The increase of the diffusion coefficient at higher temperatures results from the increase of the kinetic energy of the polymer chains. Hence, they are easier capable of giving way for diffusing molecules, which allows for more possible paths for molecules of water to move through the network [12,15]. Further, with increasing temperature the hole free-volume of the polymer increases, thus there are also more possible paths for a penetrant molecule to find a way through the polymer [14,16]. In Fig. 6 the absorption isotherm at 85 °C for the studied PVB and the fit according to the ENSIC model is depicted. As expected it shows a Type III isotherm [19]. The sum of squares for the fit was 0.27602. Also, as seen in Fig. 7, Henry's law was fitted with the assumption of 0% moisture content at 0% r.H. and the determined moisture content at 95% r.H. in accordance with the procedure in other publications [6]. The sum of squares for the resulting fit was 12.81 hence it was 2 orders of magnitude worse than the fit according to the ENSIC model. The largest deviation between Henry's law and the experimentally determined values were at a ¼0.5 with a difference of 1.41% moisture content by weight. A basic assumption for Henry's law is an ideal solution, which means no interaction between the matrix and the molecules solved and no interaction between the solved molecules is assumed. This assumption does not hold for PVB, thus the deviation of the experimental data from Henry's law can be explained. Polyvinyl butyral is a highly polar material. Due to its molecular structure, there are many available sites for water molecules to form hydrogen bonds with. Especially at higher activities water molecules can also start to interact with each other. The ratio between ks and kp, see Table 2, gives a hint that interaction of water molecules with the PVB seems to be more important than the interaction between water molecules themselves [14].
Fig. 5. Temperature dependence of the diffusion coefficient D, measured at 25 °C, 35 °C, 45 °C and 50 °C, D was determined according to the method used by Köhl et al. [7].
Fig. 6. Fit according to ENSIC model, see Eq. (6).
Fig. 7. Linear fit in accordance with Henry's law to the absorption data from the experiment, Eq. (4) was used to fit the data.
Table 2 Experimentally obtained material parameters for diffusion and absorption for PVB.
Da exp (
Fig. 4. Experimental results for the absorption experiment at 95% r.H.
ED ) RT
Da = 8.65·10−4 m2/s ED ¼ 19.19 J/mol K
aeq = KH ·Ceq KH = 4.65
ϕ=
e(ks − kp ) a − 1 (ks − kp ) / kp
kp = 3.61
ks = 0.96029
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27
A
100,00 mm
100,00 mm
Fig. 8. Area marked by the dotted line represents the FEM model as described in the methods part. Data were extracted along path A.
Fig. 9. Simulation results for constant diffusion coefficient and boundary conditions according to the assumption of Henry's law, each curve represents the moisture distribution over time at a certain depth within the sample. With the topmost curve being furthest to the edge and the lowest being the innermost spot.
Fig. 8 shows along which path the following data was extracted from the simulation of the laminates. Path A starts in the corner, which is defined as x ¼0, and ends in the middle of the laminate. In Fig. 9 the results for the simulation at 50% r.H. with boundary conditions according to Henry's law are shown. Even after 8000 h the equilibrium was not yet reached in the center of the sample. Fig. 10 shows the results of the simulation with boundary conditions according to the ENSIC model at 50% r.H. After 8000 h the equilibrium in the center was not yet reached. Both results were compared as shown in Fig. 11. The graph plotted depicts the ratio between both according to
(ωHenry − ωENSIC )/ωHenry,
Fig. 10. Simulation results for constant diffusion coefficient and boundary conditions according to the assumption of ENSIC model, each curve represents the moisture distribution over time at a certain depth in mm within the sample. With the topmost curve being furthest to the edge and the lowest being the innermost spot.
Fig. 11. Comparison of the simulation results for constant diffusion coefficient and boundary conditions according to the assumption of Henry's law and the ENSIC model, each curve represents the relative difference over time at a certain depth in mm within the sample. The arrow indicates which curve is furthest outside, with curves towards the end of the arrow are closer to the middle of the sample.
at this point is 3.2·105% with a moisture content of 1E-8 with Henry's law and 3.217E-5 with the ENSIC model. According to Eqs. (1) and (2) one would expect that the laminate with the higher gradient, which is the one with boundary conditions according to Henry's law, reaches equilibrium faster. But the simulation showed that the equilibrium is reached faster with the boundary conditions according to the ENSIC model, representing the model with the smaller gradient.
(11)
with ωHenry being the moisture content from the simulation with Henry's law and ωENSIC being the moisture content from the simulation with the ENSIC model. On one hand there is the difference between both models when they both have reached equilibrium. There is a resulting difference in moisture content between both models at equilibrium of 1.41% moisture by weight, both results differ by this value close to the perimeter where equilibrium is obtained within 8000 h. Additional comparison of the simulations shows when approaching 1000 h the moisture content in the laminate with boundary conditions according to the ENSIC model becomes higher than in the laminate simulation according to Henry's law. This difference becomes higher when coming closer to the center of the laminate (Figs. 8 and 11). This difference reaches its maximum at 1060 h for the results at a depth of 70 mm. The difference
5. Conclusions The standard method to determine the moisture uptake for a polymer in the PV research literature is to calculate the sorptivity from permeation experiments at 100% r.H. This only allows for the application of Henry's Law, but as we could see this does not necessarily hold for every polymer used in the PV sector. And although on first sight it appears that Henry's Law is a viable option for a worst case scenario. The simulations showed that it does not in every case deliver the highest moisture content for a given depth and time. At an ingression depth of 20mm up to the center for a glass– glass-laminate of 100 mm by 100 mm the moisture concentration actually is higher with the lower boundary conditions at 50% r.H. While the lower boundary conditions are connected to the usage of the ENSIC model in this case. When this ratio is scaled up to
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larger areas specimens this would mean that from 25% of the way from the corner to the center the moisture content is higher than expected from the approach with Henry's law. When taking into consideration the low tolerance against moisture for certain coming PV technologies and also for thin-film PV in general, this can have a huge impact in the predictability of simulations. When performing simulations with climate data that have constant intermediate relative humidity, this means between 30% r.H. and 70% r.H., for timescales of 500 h and 2000 h. As is the case for the humid continental climates for example. For arid or tropical climates in contrast the difference would not be so important because they have a constant high or low humidity an equilibrium would be reached where Henry's law and the ENSIC model are nearly in agreement, see Fig. 7.
Acknowledgments Gratefully acknowledged is the funding of the project S-PAC, grant number 03WKBW05C, by German Ministry for Education and research BMBF.
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