A Comparative Study of Calorimetric Methods to

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stack. Placed on both sides of the PV cells, the elastomeric encapsulant provides structural support by limiting these ..... plex mixture of crosslinking agents while on the bottom the 32 ..... 46 R. Alamo, E. Chan, L. Mandelkern, I. Voigt-Martin.
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A Comparative Study of Calorimetric Methods to Determine the Crosslinking Degree of the Ethylene-Co-Vinyl Acetate Polymer Used as a Photovoltaic Encapsulant phane Ogier,1,2,3,4,5 Chloe  Vidal,4 David Chapron,2,3 Patrice Bourson,2,3 Isabelle Royaud,4 Ste 4 1,6 Marc Ponc¸ot, Marion Vite, Manuel Hidalgo5,6 1

Department of Solar Technologies, Univ. Grenoble Alpes, INES, F-73375 Le Bourget du Lac, France, CEA, LITEN, Le Bourget du Lac, F-73375, France 2  de Lorraine, EA n84423, 2 rue Edouard Belin, Metz, 57070, France LMOPS, Universite 3 lec, 2 rue Edouard Belin, Metz, 57070, France LMOPS, Centrale-Supe 4  de Lorraine, UMR 7198 CNRS, Parc de Saurupt CS 50840, Nancy, 54011, France Institut Jean Lamour (IJL), Universite 5 nite, 69310, France Arkema-CRRA, Rue Henri Moissan, Pierre-Be 6  man, 73375 Le Bourget du Lac, France SOLLIA, Joint lab. ARKEMA-CEA, LITEN, Dept. of Solar Tech, INES, 50 avenue du Lac Le Correspondence to: S. Ogier (E-mail: [email protected]) Received 2 December 2016; accepted 27 February 2017; published online 00 Month 2017 DOI: 10.1002/polb.24335

ABSTRACT: EVA copolymer foils are widely used as encapsulants for photovoltaic (PV) cells in PV modules. These foils need to be crosslinked during module manufacturing, to enhance their properties. Accurate and reliable methods for the determination of their crosslinking degree are thus very important. In this work, two semi-empirical calorimetric methods are considered and compared to a scientifically sound rheological method used as a reference. The main purpose of this work is to reveal the chemical and physical fundamentals on which the two calorimetric methods are based, to allow for a scientific understanding of their advantages, and limitations. For one of

these calorimetric methods, the so-called “Melt-Freeze” method, we have sought for a deeper understanding of the underlying crystallization physics through the use of successive selfnucleation and annealing experiments, which give access to the crystallite size distribution of EVA, and to the influence of C 2017 Wiley Periodicals, Inc. J. Polym. crosslinking upon it. V Sci., Part B: Polym. Phys. 2017, 00, 000–000

INTRODUCTION The global photovoltaic (PV) market is growing year after year. With the aim of staying competitive with respect to other energies, durability and reliability of PV modules remain the key subjects.1–3 This requires consistent quick methods to characterize materials. Throughout the PV modules lifetime, weathering implies temperature gradients and causes differential thermal expansions within the PV stack. Placed on both sides of the PV cells, the elastomeric encapsulant provides structural support by limiting these expansions. It also supplies a mechanical and electrical protection as well as insulation from environmental stresses (moisture, oxygen, etc.).

by less-expensive resins has been studied since the early 1980s. This led to the emergence as PV encapsulants, of carbon backbone polymers which are cheaper due to their accessibility from hydrocarbons.

As stated by Kempe and Cuddihy et al.,4–6 the first PV encapsulant resins developed in the 1960s were essentially based on polydimethyl siloxane (PDMS). The photo-thermal stability of silicones made them the ideal PV encapsulants. However, to reduce PV module price, the replacement of silicones

crosslinking; differential scanning calorimetry; encapsulant; ethylene and vinyl acetate; photovoltaic; rheology

KEYWORDS:

Nowadays, the dominating encapsulant is by far, a semicrystalline copolymer of ethylene and vinyl acetate (EVA).7,8 During the so-called lamination process, the EVA foils are melted to protect the PV cells and to hold together all the module components. This hot pressing process triggers the EVA crosslinking since the foils contain a crosslinking agent (organic peroxide) which decomposes at the lamination temperature. The crosslinking reaction leads to a three dimensional network; this happens through the creation of intermolecular chemical links between EVA copolymer chains .9–11 Crosslinking enhances the thermomechanical properties of EVA and thus limits its creep (or “cold-flow”) with time.12 It

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also improves its chemical-resistance and optical properties.13–16 When the level of crosslinking is insufficient, the EVA encapsulant may creep at the upper bounds of the working (on-field) temperature of PV modules; this is undesirable, because it might lead to internal movement of the PV cells, thus creating mechanical stress. In some extreme cases (e.g., glass/glass unframed modules), the creeping encapsulant can even exit the module. This is one of the reasons why PV module manufacturers need to constantly monitor the degree, or level, of crosslinking of the EVA encapsulant.17,18 Prior efforts have been made to develop an easy way to determine the crosslinking degree (%XL) of EVA encapsulants. Several methods have been developed over the past decades. Two categories can be established: on one hand, the “direct” methods which can be related to the actual crosslinking density, and in the other, the more “indirect” methods which measure a property that can be correlated with the crosslinking density. Among the latter, the gold standard of industry for measuring the level of crosslinking, is the solvent extraction method, known as the “gel-content” method. In the so-called “direct” methods category, the equilibrium swelling of polymers,10,19–22 osmometry,21,23 and the measurement of mechanical properties (modulus) have been reported as being those that can give access to the actual crosslinking density. 20,24–27 However, these methods take long time, can be complex and may require toxic chemicals. The need to use toxic chemicals in the case of swelling experiments is related to the swelling properties of EVA, a modified polyolefin, mostly compatible with aromatic solvents. These drawbacks make the use of direct methods, difficult to apply in the PV industry.28 The second category is that of, the more “indirect” methods, which have been developed to be more user-friendly. Several of these “indirect” methods, including the most widelyknown “gel-content” method, have been summarized by Hirschl et al.28 Besides the “gel-content” method which suffers from the same drawback as the direct swelling-method (need to use toxic chemicals),12 the authors give an insight on the underlying principles around more than a dozen other techniques.28 Among them, differential scanning calorimetry (DSC), rheology, spectroscopy (UV-Visible, Infrared, Raman), acoustics and mechanical indentation can be mentioned. The objective of this study is to compare the results obtained using several recently developed methods for the evaluation of the crosslinking degree of EVA, and to investigate the relation between the method performances and the physical properties (i.e., crystallinity) of the crosslinked copolymer. It must be noted that the aforementioned indirect methods provide an estimate of the crosslinking degree of the copolymer rather than the real crosslinking density. Two of them, are based on calorimetric measurements (DSC). DSC is an easy-to-use technique which can detect all thermal events related to the physical and chemical transformations

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of the material (melting, crystallization, glass transition, chemical reactions). Moreover, recently developed DSC techniques, such as successive self-nucleation and annealing (for SSA), can give access to more subtle details, such as the crystallite size-distribution, and its changes as a result of the crosslinking reaction.29–32 Rheological measurements can also be used to determine the crosslinking degree of EVA and could even be used as a direct method for the determination of the crosslinking density Indeed, rheological measurements provide values for the mechanical moduli, which according to the mechanical theory of rubber elasticity are directly related to crosslinking density, defined as the number of moles of elastically active chains per unit volume.14,15,33 Because of the close relation between rheological measurements (mechanical moduli), and crosslinking density this technique is used as the reference method in this paper.

EXPERIMENTAL

Materials Two EVA commercial PV films were studied: those containing 28 wt % or 32 wt % of vinyl acetate-derived units (VA) R 15685 P and PhotocapV R 15420 P/UF, respectivePhotocapV ly; these materials were supplied by STR (Spain).The 32 wt % VA polymer foils are c. 450 mm thick while the 28 wt % VA ones are c. 200-mm thick. The EVA samples (100 cm2 total surface) were cured using a 3S PV laminator (model S1815E), while placed between two polytetrafluoroethylene (PTFE) sheets, with the whole stack resting upon a 3 mmthick glass plate. This configuration is intended to be close to an actual PV-module glass/backsheet-type of stack. Figure 1 features a schematic drawing describing the different steps of the lamination process. The EVA films underwent different thermal treatments leading to a wide range of crosslinking (XL) degrees. The curing step was carried out at 150 8C for 3, 4, 5, 6, 8, and 10 min. The degassing step lasted always 2 min, and the cooling step ended when the PV module regained room temperature. Methods For the Melt/Freeze and Residual Enthalpy methods described below, a TA Instruments Q20 calorimeter was used, while for the SSA method a TA Instruments Q200 calorimeter was used. In both cases, samples weighed in between 3 and 10 mg, and the heating or cooling rate was 10 8C min21. DSC Residual Enthalpy (RE) Method The so-called RE method is performed by heating the sample from room temperature to 200 8C. This method, first described by Xia et al., considers the relative ratio of exothermic enthalpies between a given sample and its uncured equivalent in the temperature range of the crosslinking reaction (between 100 8C and 200 8C).34,35 Further details on how to use this method can be found in Refs. 34–36.

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selected temperature (TS) as defined by the self-nucleation (SN) protocol developed by Fillon et al.39 The SN protocol comprises the following steps: 1. The thermal history of the sample is deleted by heating it up to a temperature around 25 8C above the melting temperature (Tm) and by holding this temperature (in our case 100 8C) for 5 min before cooling down to room temperature (in our case 25 8C) at a cooling rate of 10 8C min21. 2. Heating at 10 8C min21 to a selected temperature (TS) higher than the end-temperature of the melting range of EVA (revealed by step 1). Typically this end-temperature is comprised in between 70 8C and 90 8C for PV grade EVA. The sample is held at this temperature for 5 min. 3. Cooling down to 25 8C at 10 8C min21. 4. The first three steps of the procedure are repeated while decreasing TS at each loop by 1 8C until it reaches a temperature 5 8C below the melting temperature Tm. The SN protocol reveals three domains on the melting peak, separated by temperatures TS1 and TS2 as shown in Figure 2. The following description of these three domains allows to understand how TS1 and TS2 were determined. Domain I: TS > TS1. Complete melting is supposed to occur. No residual nuclei should be left. This is reflected by the fact that the ensuing recrystallization always takes place at the same temperature range. As long as the recrystallization curves superpose, one can consider that the sample remains in Domain I (DI). FIGURE 1 The different steps of the lamination process: (1) The PV module is heated under vacuum, while initially resting upon a set of pins; gas from still solid EVA foils is thus evacuated under vacuum. (2) The pins are down, and a pressure of around 1 atm is applied on the PV module which comes in direct contact with the heating plate; (3) After the lamination process, the PV module is taken out and it is allowed to cool down to room temperature. [Color figure can be viewed at wileyonlinelibrary.com]

DSC Melt/Freeze (MF) Method The so-called MF method developed by Hidalgo et al.37,38 is run by heating the samples to 100 8C, and then cooling them down from 100 8C to 220 8C.35 This method based on the fact that EVA, as a semi-crystalline copolymer, crystallizes upon cooling from the molten state, takes into account three parameters: the temperature where crystallization begins (Tonset), the temperature at the top of the crystallization peak (Tc), and an empirical shape factor (SF) for the crystallization peak calculated according to the procedure described in Refs. 35,37,38. The average of the normalized evolution of these three parameters is used as an empirical indication of the degree of crosslinking of the samples. Successive Self-Nucleation and Annealing SSA experiments, first proposed by Arnal et al.,29 were performed to evaluate the impact of the EVA crosslinking upon the size distribution of the crystallites present in the samples. SSA is a thermal fractionation technique which uses a

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Domain II: when TS1 > TS > TS2, partial melting occurs. A decrease in TS translates into a shift of the subsequent

FIGURE 2 Thermogram of the melting region of 28 wt % VA EVA, showing the three domains as obtained from the SN protocol—step (1). The determination of the temperature TS2 is necessary to trigger the SSA protocol explained below. It is the latter which permits to analyze the crystallite size distribution of the EVA copolymer. Note that the exo down convention is used here. [Color figure can be viewed at wileyonlinelibrary.com]

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FIGURE 3 (a) Thermograms from the SN protocol for 28 wt % VA EVA. It allows to determine three domains on the melting region. (b) Endotherms of melting influenced by the different annealing thermal treatments. This zone helps to determine the temperature TS2. (c) Exotherms of crystallization also influenced by different annealing thermal treatments. This zone helps to determine the temperature TS1. Note that the exo down convention is used here. [Color figure can be viewed at wileyonlinelibrary.com]

recrystallization peak towards higher temperatures. The origin of this shift will be discussed in the following sections. Domain III: at TS < TS2, a partial melting is still occurring and the remaining crystals are subjected to annealing. Due to the annealing, the DSC thermogram can be modified in several ways with the most apparent change being the emergence of a second melting peak during step 1 (deletion of the thermal history) of the cycling procedure (cf. Fig. 3). Once TS1 and TS2 are defined, the actual fractionation protocol (i.e., SSA) can be implemented. This is done as follows: 1. Carrying out a first step which is exactly the same as the first step of the SN protocol. 2. Heating to an initial TS temperature, which should be slightly above (e.g., 1 8C) TS2, and remaining at this temperature during 5 min. 3. Cooling down to 25 8C at a rate of 10 8C min21. 4. Heating up to a new TS which should be 5 8C lower than the previous one and remaining for 5 min. 5. Repeating steps (3) and (4) until TS reaches the initial TS temperature minus 50 8C (i.e., 10 loops of 5 8C). 6. Carrying out a final heating, up to 100 8C to melt all the fractionated crystals. This procedure is depicted in Figure 4. Determination of the Equilibrium Melting Temperature Tm0 Tm0 is necessary for the calculation of the crystallite sizes as explained below. To determine Tm0, uncured EVA samples

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are subjected to several thermal cycling treatments in the DSC Q200 TA Instruments going from 0 8C through 100 8C with different heating/cooling rates from 5 8C min21 up to 50 8C min21. Rheological Measurements The rheological measurements were carried out on 25 mm diameter discs of EVA, using an Anton Paar Physica MCR 302 rheometer in a parallel-plates configuration and in the shear oscillatory mode. The temperature was fixed at 100 8C and a frequency sweep between 100 Hz and 0.1 Hz was conducted. From these experiments, one determines the values

FIGURE 4 Temperature versus time profile for the SSA crystal fractionation method. TS1 is defined as the upper limit of the melting range temperature as described in the SN protocol. The initial TS temperature of the SSA protocol is chosen to be just above (c. 1 8C) TS2. [Color figure can be viewed at wileyonlinelibrary.com]

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TABLE 1 Peak Crystallization and Melting Temperatures of Both Uncured EVA Samples with 28 and 32 wt % VA

FIGURE 5 Evolution of the loss factor tan d at 1 Hz of both EVA’s (28 and 32 wt % VA). This method allows to determine the reference crosslinking degree of the EVA samples. The points in the curves of this figure correspond to lamination times going from 3 to 15 min. [Color figure can be viewed at wileyonlinelibrary.com]

of the elastic, G0 , and viscous, G”, components of the complex shear modulus. As described elsewhere, we use the value of tan d 5 G/G0 at 1 Hz to characterize the degree of crosslinking (cf. Fig. 5).34,36,37 RESULTS AND DISCUSSION

A typical DSC thermogram of the 32 wt % VA EVA is shown in Figure 6. Three thermal phenomena occur: during the first heating step, the endothermal phenomenon of melting (note that in this thermogram the exo up convention is used) appears as a long temperature-range transition with a peak

Sample

Tc (8C)

Tm (8C)

Uncured EVA 28 wt % VA

53.0

72.6

Uncured EVA 32 wt % VA

45.6

66.8

between 60 8C and 80 8C (depending on the VA content and the crosslinking degree); then at higher temperature, around 150 8C, the exothermal peak of the crosslinking agent decomposition, and the simultaneous crosslinking reaction occur. Finally, an exothermal peak takes place when the EVA is cooled from its melted state: the crystallization phenomenon occurs with a peak situated between 55 8C and 45 8C (also depending on the VA content and the crosslinking degree). Crystallization and melting temperatures of both uncured 28 and 32 wt % VA EVA’s are shown in Table 1. In the following sections, both the RE and MF calorimetric methods based upon the analysis of the exothermal phenomena, are discussed.

The Residual Enthalpy Method (RE) The so-called RE technique uses the enthalpy of crosslinking of EVA as the to-be-followed parameter to monitor the conversion rate of this chemical reaction. An uncured EVA shows, when submitted to a DSC heating ramp up to c. 200 8C, a maximal enthalpy, coming majorly from the decomposition of practically the total amount of crosslinking agent present in the sample. The crosslinking reaction, which is exothermic itself can contribute slightly to the total measured enthalpy, but the major contribution comes from the decomposition of the crosslinking agent(s). On the contrary, a fully crosslinked EVA shows a minimum or no more enthalpy, when submitted to the DSC experiment due to the fact that there is little or no crosslinking agent remaining in the sample after it has undergone crosslinking during the lamination process (cf. Fig. 7). The RE method considers a linear relationship between the crosslinking degree, and the remaining (or residual) enthalpy: %XLRE 5

FIGURE 6 DSC thermogram of a non-crosslinked EVA (32 wt % VA content) with a 10 8C min21 heating and cooling rate. The sample was firstly melted up to 100 8C, and recrystallized by cooling down to 220 8C; then it was heated up to 225 8C in a second heating step (only the second heating step is shown in the figure). [Color figure can be viewed at wileyonlinelibrary.com]

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DHuXL 2DHL DHuXL 2DHfXL

(1)

where DHuXL is the enthalpy of the uncured EVA, DHfXL is the enthalpy of fully crosslinked EVA and DHL is the enthalpy of a partially crosslinked sample with an unknown degree of crosslinking. In some cases, the fully crosslinked EVA sample shows no more enthalpy due to a complete decomposition of the crosslinking agent during lamination, that is, DHfXL 5 0 J mol21. In this case, eq 1 becomes:

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FIGURE 7 Reduction of the enthalpy of the crosslinking agent for the 32 wt % VA EVA sample. The residual enthalpy is used for the determination of the crosslinking degree by the RE method. The decomposition of crosslinking agents occurs during the lamination process and triggers the crosslinking reaction. [Color figure can be viewed at wileyonlinelibrary.com]

%XLRE 5

DHuXL 2DHL DHuXL

(2)

We have found that, EVA films may feature more or less complex mixtures of crosslinking agents as shown in Figure 8. This implies that the depletion of the more complex mixtures might follow a non-linear behavior, inducing some error in the estimation of the crosslinking degree. To confirm or disprove the hypothesis of a non-linear depletion of crosslinking agents, a simulation of a first-order

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FIGURE 9 Temperature versus time profile during the lamination process depicted in Figure 1. [Color figure can be viewed at wileyonlinelibrary.com]

peroxide decomposition has been used to compare with the residual enthalpies obtained with DSC measurements. For that, the same thermal treatment monitored during the lamination process (as described in Fig. 9) was applied to a standard first-order kinetic decomposition of different peroxides which have been reported in the literature as possible candidates for the crosslinking of EVA. The first-order kinetics decomposition constant for a given peroxide at different temperatures can be obtained by deducing the activation energy from decomposition half-life data available in the literature.40 For each iteration of a Dt time (and thus for a mean temperature of DT), the isothermal decomposition kinetic constant of the peroxide kd can be determined. It is thus possible to evaluate the peroxide decomposition yield a as a function of time/temperature as follows: ½I 5½I 0 :eð2kd tÞ

(3)

½I 0 2½I  5a ½I 0

(4)

where ½I 0 is the initial concentration of the “initiator” of the crosslinking reaction (i.e., the peroxidic crosslinking agent), ½I  is the concentration of the peroxide decomposed at time t, and a is the decomposition yield at time t. The comparison between the residual enthalpies obtained by the RE method and a is shown in Figure 10.

FIGURE 8 Two DSC thermograms for initially uncured EVA samples. On the top, the 28 wt % VA EVA reveals a very complex mixture of crosslinking agents while on the bottom the 32 wt % VA EVA shows a simpler and large enthalpy peak. [Color figure can be viewed at wileyonlinelibrary.com]

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The residual enthalpies for the 32 wt % VA EVA, likely containing a relatively simple crosslinking agent formulation, is in agreement with the first-order kinetics decomposition yield a for a single peroxide (coefficient of determination R2 5 0.91). The residual enthalpies of the 28 wt % VA EVA, with a complex crosslinking agents formulation, do not fit as well as for the 32 wt % VA EVA (with a R2 5 0.88). Moreover, a nonlinear trend is found in the latter case. This trend might result, for example, from the mixture of two or more

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FIGURE 10 The residual enthalpy obtained from the RE method for the 32% wt. VA EVA with a rather simple crosslinking agent formulation, and that for the 28 wt % VA EVA with a much more complex mixture of crosslinking agents, as a function of a first-order decomposition yield a corresponding to the kinetics of a single peroxide. The coefficient of determination in italics corresponds to a second-order polynomial fit equation. [Color figure can be viewed at wileyonlinelibrary.com]

different crosslinking agents, each decomposing with firstorder kinetics at different rates (different kd’s). Indeed, some commercial EVA films contain a complex mixture of crosslinking agents, the presence of which can explain the departure from simple first-order kinetics behavior. The residual enthalpies are then compared to the rheological measurements (tan d at 1 Hz) used as the reference method (Fig. 11). It can be observed that the crosslinking reaction is complete when the value of tan d is below 0.2. For the 28 wt % VA EVA, the evolution of the residual enthalpy as a function of the lamination time is in good agreement with the rheological measurements (R2 5 0.94), while for the 32 wt % VA EVA, the correlation is poor (R2 5 0.61). This could be explained by the presence of an excess of crosslinking agent in the 32 wt % VA EVA: when the latter is fully crosslinked (which can be assumed by the fact that the rheological measurements reach a limit value at around 0.2 for tan d at 1 Hz), the sample still contains a non-negligible amount of crosslinking agents. The consequence of this can be the continuous fall in residual enthalpy with no further effect on the actual (as measured by rheology) crosslinking degree. As a result, the correlation between the RE evaluation, and that of the rheological method is bad. On the other hand, for the 28 wt % VA EVA, for which the RE analysis of the uncured sample revealed a complex mixture of crosslinking agents, this seems not to interfere with the evaluation of the crosslinking degree by this RE method. The Melt/Freeze Method (MF) The MF method considers the crystallization phase-transition, which reflects the influence of the EVA crosslinking. This method is based on three parameters, which describe the evolution of the crystallization peak: the Tonset temperature where

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FIGURE 11 Comparison between the residual enthalpies deduced from the DSC measurements and the values of tan d at 1 Hz obtained by the rheological method for both 28 and 32 wt % VA EVA samples. Both EVA are fully crosslinked (fXL) when tan d at 1 Hz is below 0.2, according to previous results.36 The difference from the linear trend is evident for the 32 wt % VA sample, showing a lack of accuracy, and precision using the RE method with this particular sample. [Color figure can be viewed at wileyonlinelibrary.com]

crystallization begins, the TC crystallization peak temperature, and the SF, corresponding to a peak shape factor (cf. Fig. 12). The SF is supposed to be influenced by the formation of small crystallites while Tc and Tonset are more sensitive to the bigger crystallites. The crystallites in EVA copolymers are quasi exclusively composed of ethylene co-units, since the more bulky VA-derived units are supposed to be rejected as defaults into the amorphous phase.41 The MF method uses the average of the normalized crosslinking degrees obtained from the three parameters, as following:

FIGURE 12 Crystallization thermograms of the 32 wt % VA EVA with different crosslinking degrees, and description of the three parameters used in the MF method.37 [Color figure can be viewed at wileyonlinelibrary.com]

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TABLE 2 Determination Coefficients (R2) for the Correlations of Either the MF or the RE Method, with the Reference Rheological (tan d) Method, for Five Other Commercial PV Encapsulant Films R2 comparison

FIGURE 13 Comparison between crosslinking degrees (%XL) obtained by the MF method and the rheological measurements of tan d at 1 Hz for both 28 and 32 wt % VA EVA. Both EVA’s are considered as fully crosslinked (fXL) when tan d at 1 Hz is below 0.2.36 [Color figure can be viewed at wileyonlinelibrary. com]

ð%XLTc 1%XLTonset 1%XLSF Þ %XLMF 5 3 with %XLY 5

YuXL 2YL 3100 YuXL 2YfXL

(5)

%XL MF vs. tan d

%XL RE vs. tan d

EVA33 1

0.97

0.85

EVA33 2

0.90

0.77

EVA28 1

0.92

0.98

EVA28 2

0.92

0.67

EVA28 3

0.95

0.87

From the previous results, the SSA technique is used to show the influence of the crosslinking reaction on the crystallite size distribution. The choice of the first TS for the SSA protocol is very important. Ideally, the first TS has to be high enough to melt most of the crystallites but low enough to let some crystal fragments which will play as non-melted nuclei during tS 5 5 min. It has to be noticed that these “residual” fragments or nuclei are controversial according to Reid et al. and M€ uller et al.32,42 From their point of view, there is no need to have crystal fragments for the self-nucleation, only crystalline memory is enough to explain this phenomenon.

(6)

and Y5Tc ; Tonset ; and SF. To evaluate the reliability of the MF method, the crosslinking degree measurements of both 28 and 32 wt % VA EVA were calculated and plotted as a function of the values of tan d at 1 Hz evaluated by the rheological measurements (Fig. 13). For both EVA, the fit between the MF method and the rheological method is acceptable (with a determination factor close to 0.9), considering that experimental error on commercial samples plays a role in the results’ scatter. The MF method provides results which are independent from the type of mixture of crosslinking agents, but also from the total amount of them in the initial EVA film. From the authors’ experience, the MF method usually performs better, when compared to rheology, than the RE method. This is illustrated by the results shown in Table 2, where, for different commercial encapsulants, the determination coefficients are listed for the linear correlation between the DSC methods, and the rheological method used as a reference. More on this can be found in Refs. [36-38].

Determination of the Crystallite Size Distribution: A Physical Basis for the MF Method To highlight the change of the crystallite size distribution after the crosslinking reaction, the SN protocol is necessary before starting the SSA protocol. The determination of the three domains of melting of both EVA samples is done using the SN protocol (cf. Table 3).

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Several samples of EVA with a widespread range of crosslinking degrees, as evaluated by rheology have been analyzed with the SSA protocol described above. The last heating run of these protocols, the one that ultimately reveals the crystals size-distribution is shown in Figure 14 for the 28 wt % VA EVA. The deconvolution of the fractionated thermograms of EVA R (v. 0.9.8) software leads to a series of using the FytikV Gaussian distributions as the best fitting model for the SSA fractionation thermograms (cf. Fig. 14). Then, with the help of the Gibbs-Thomson equation,41,43–45 it is possible to evaluate the mean crystallite size dc for each temperature peak of the fractionation thermogram: dc 5

0 2 : r : Tm : Dz  0 Dh : Tm 2Tm

(7)

where the free enthalpy of lamella surface is r 5 5.0 kJ mol21, the enthalpy of melting of the C2H4 group is Dh 5 8.2 kJ mol21, the unit length of the C2H4 group in the chain

TABLE 3 Selected Temperatures TS1 and TS2 for Both 28% and 32%wt. VA EVA; These Temperatures Delimit the Three Domains Observed During Melting (cf. Fig. 2) Sample

TS1 (8C)

TS2 (8C)

EVA 28 wt % VA

86

83

EVA 32 wt % VA

82

77

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0 TABLE 4 Equilibrium Melting Temperatures Tm for Both 28% and 32%wt. VA EVA from the Hoffman-Weeks Extrapolation

FIGURE 14 Melting part of the thermograms for the 28 wt % VA EVA at several crosslinking degrees (determined by the rheological method) after applying the SSA protocol. Only the last heating run is shown in this graph. Note that the exo down convention is used here. [Color figure can be viewed at wileyonlinelibrary.com]

Sample

Tm0 (8C)

EVA 28 wt % VA

77

EVA 32 wt % VA

75

It has to be noticed that we have used a constant thickening factor b 5 1 in the Hoffman-Weeks equation 6. The limitations of this equation are discussed in several references.46,48,49   1 1 0 Tm ðxb Þ5 Tc ðxb Þ1 12 Tm ðx b Þ (8) b b where xb is the molar ratio of VA comonomer. Results for both EVA are shown in Table 4.

direction is Dz 5 0.254 nm.43,44 The equilibrium melting temperature of the pure crystallite Tm0 is deduced from the Hoffman-Weeks extrapolation 46–49 by plotting the melting temperature as a function of the crystallization temperature, obtained using the heating/cooling varying rate procedure described in the experimental section. The intersection of the extrapolated plot with the Tm 5 Tc line gives the actual Tm0 as shown in Figure 15.

Finally, the crystallite size distribution is evaluated from the enthalpy measured from the area under each temperature peak of the fractionation thermograms. The deconvolution procedure allows to obtain the crystallite proportion as the ratio between the surface under a given Gaussian distribution and the sum of the areas for all Gaussian distributions. The plot of the size-distribution for the 32 wt % VA EVA is shown in Figure 16. A tightening of the crystallite size distribution towards smaller sizes is observed when the samples are more and more crosslinked. The same results are observed with the 28 wt % VA EVA.

FIGURE 15 Melting temperature as a function of the crystallization temperature for the EVA 28 wt % VA EVA at several heating/cooling rates. The equilibrium melting temperature Tm0 can be deduced from the extrapolation of Tm up to Tm0 with the Hoffman-Weeks equation (6) as described below. [Color figure can be viewed at wileyonlinelibrary.com]

FIGURE 16 Crystallite size distributions for the 32 wt % VA EVA with various crosslinking degrees. This graph is obtained from the SSA protocol with the help of the Gibbs-Thomson equation. The crystallite proportion for a given crystallite thickness corresponds to the fraction of the total crystallinity for that crystallite size. [Color figure can be viewed at wileyonlinelibrary.com]

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Further characterizations of the crystalline part of semicrystalline EVA for PV applications, and its evolution as a result of different levels of crosslinking, can be carried out also using other experimental techniques such as the Raman spectroscopic method longitudinal acoustical mode (LAM),46,50–54 small angle X-Ray scattering (SAXS),46 or even transmission electron microscopy (TEM) images.51,55 The comparison of the results obtained with these techniques to those obtained here would be useful to confirm the trend observed with the SSA protocol. CONCLUSIONS

Several techniques allow to evaluate the crosslinking degree of EVA. A few of them are directly linked to crosslinking densities but they are rather complex and require experimental expertise. On the other hand, DSC methods are fast and easy to use. Concerning the actual performance of these very easy-to-use semi-empirical DSC methods, we have found here that for the RE method the fit is very much dependent on the type of EVA grade under examination. Thus, for example, a large excess of crosslinking agents in the initial EVA foils may lead to inaccurate evaluations of the crosslinking degree when using this method. The MF method, which is linked to the crystalline structure of the samples and its evolution as a function of the crosslinking degree is less dependent on the EVA grade, and often fits much better with the reference measurements from rheology. We explored here the physical background of the MF method, which has been shown to be that of the decrease of the average size, and the narrowing of the size distribution of crystallites, due to the increase of the crosslinking level.

ACKNOWLEDGMENTS

This project has received support from the State Program “Investment for the Future” bearing the reference ANR 210ITE-0003.

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