Water Vapor Sorption Properties of Polyethylene Terephthalate over a

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Water Vapour Sorption Properties of Polyethylene Terephtalate over a Wide Range of Humidity and Temperature Florence Dubelley, Emilie Planes, Corine Bas, Emmanuelle Pons, Bernard Yrieix, and Lionel Flandin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b11700 • Publication Date (Web): 25 Jan 2017 Downloaded from http://pubs.acs.org on January 25, 2017

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The Journal of Physical Chemistry

Water Vapor Sorption Properties of Polyethylene Terephthalate over a Wide Range of Humidity and Temperature Florence Dubelley,1,2 Emilie Planes,1,2* Corine Bas,1,2 Emmanuelle Pons,3 Bernard Yrieix3 and Lionel Flandin1,2 1

Université Savoie Mont-Blanc, LEPMI, F-73000 Chambéry 2

3

CNRS, LEPMI, F-38000 Grenoble, France

EDF R&D, Materials and Mechanics of Components, Ecuelles, F-77818 Moret-sur-Loing Cedex, France

*Corresponding author: [email protected] (E.Planes)

ABSTRACT

The dynamic and equilibrium water vapor sorption properties of amorphous polyethylene terephthalate were determined via gravimetric analysis over a wide range of temperature (2370 °C) and humidity (0-90 %RH). At low temperature and relative humidity, the dynamics of the sorption process was Fickian. Increasing temperature or relative humidity induced a distinct up-

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swing effect, which was associated to a plasticization/clustering phenomenon. For high temperatures and relative humidity, a densification of the polymer was evidenced. In addition to the classical Fickian diffusion, a new parameter was introduced to express the structural modifications of PET. Finally, two partial pressures are defined as thresholds that control the transition between these three phases. A simplified state diagram was finally proposed. In addition, the thermal dependence of these sorption modes was also determined and reported. The enthalpy of Henry’s water sorption and the activation energy of diffusion were independent on vapor pressure and followed an Arrhenius law.

1. INTRODUCTION The understanding sorption and transport mechanisms of water in polymeric materials are major importance. It is a complex phenomenon, because the sorption might alter the structure of the materials. Penetrant molecules may for instance plasticize glassy polymers Tg generally associated with a decrease in glass transition temperature stiffness and strength

11

9, 10

1-8

. This is

and degradation of

. In addition to plasticization, water clustering phenomenon in the

polymer matrix may occur. This results from self-hydrogen bonding of water molecules when absorbed in a polymer 12. Water clusters can in turn impact the diffusion of water vapor through polymer, and increase their diffusion pathway. These observations are extensively described for the sorption of gas and water in glassy polymers

13-17

. The effect of water on Polyethylene

Terephthalate (PET) is however not described in a systematic way over a wide range of temperature and humidity. PET is widely used for high barrier applications (packaging, organic light emitting diodes, organic photovoltaic module and vacuum insulation panels)

18, 19

, especially when low cost and


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good mechanical properties are additionally required by the application. Understanding the sorption and transport behavior of water in polymeric materials is important for these applications. Even if PET is defined as a hydrophobic polymer

20

, because it absorbs less than

1 % of water (g/gDRY) under saturation moisture conditions, moisture can have detrimental effects on its mechanical, thermal and barrier properties. Water permeates to a larger extent than permanent gases due to a larger solubility of water and its plasticization effect in material containing polar sites 21. Low water sensitivity seems to have been assumed from this low mass gain, and few studies have been conducted with the goal of understanding the water sorption and diffusion in PET 1, 18, 20, 22-26. Most authors measured a linear behavior between the water content of PET and the relative humidity (RH) (Fickian sorption and diffusion)

20, 27

. This expected

behavior has been observed extensively and at relatively short time scale. Very few authors however noticed that the behavior was no longer Fickian at high relative humidity and for longer interaction with water

28, 29

. Significant changes on the physical properties of polymer might

appear such as plasticization

25, 26

, water clustering

30, 31

and decrease in glass transition

temperature 24, which results in changes in solubility and diffusivity of the penetrant and makes transport highly concentration dependent 9. It is also important to note that these modifications were extremely dependent on the initial microstructure and crystallinity of the polymer (filler content and dispersion, crystallinity)

21, 24-26, 30, 32-36

. These microstructural changes can have

noticeable consequences on the barrier and mechanical properties of PET jeopardizing its service time. The present study presents a detailed investigation of sorption and diffusion properties of water in an amorphous PET by a gravimetric method over a wide range of temperature and humidity on a large temperature and relative humidity range, respectively between 23 and 70 °C and 0 to


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90 %RH. The main objective is the determination of structural modifications of PET in a wide range of temperature and humidity conditions, in order to understand the impact of water vapor and temperature on permeation mechanisms in thin films.

2. EXPERIMENTAL 2.1. Materials The base film is a polyethylene terephthalate (PET) of 280 µm in thickness. This polymer was supplied by Rexor (38, Paladru - France). It is amorphous with a glass transition temperature (Tg) close to 75 °C, as measured by DSC. The viscosity average molecular weight of the polymer was estimated at 22 kg/mol following the standard ASTM D 4603.

2.2. Experimental Kinetic gravimetric sorption experiments were performed using a DVS IGASORP instrument (Hiden Isochema). Water uptakes were performed on a small section of PET film: approximately 2-3 cm2 and 70 mg .The sample is hung on a hook to limit the condensation during the experiment. Before the sorption kinetic, the sample was first dried in DVS chamber to 0 %RH at 40 °C (below Tg) during 72 h to establish a dry mass. After dry mass was achieved, the sample was exposed at a fixed temperature to the following relative humidity (RH) profile: from 0 to 90 % in %RH increments by step of 10 or 5 %RH. Relative humidity depends of the partial pressure of water (p) and the saturation vapor pressure of water (p0): % =

× 100 1


4

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The water uptake was recorded as a function of time. A constant duration of 48 h was utilized for each RH step unless noted otherwise. This time step is already extremely long for thin films, and was sufficient to observe a mass equilibrium at low temperature and low humidity. The equilibrium mass uptake value, m48h, was used to determine the equilibrium water concentration in the polymer C (cm3(STP).cm-3(polymer)) as follows:

=

× 2 ×

Where Vm is the molar volume of water vapor (22414 cm3.mol-1), Mw the water molecular weight (18 g.mol-1) and Vp the polymer volume (cm3). Complete sorption was collected at five temperatures: 23, 40, 50, 60 and 70 °C (Figure 1). The experimental conditions were detailed in the supporting information (SI).


5


0,012 23 °C

90 %RH

mass gain (%)

0,010 0,008 0,006 0,004

0 %RH

0,002

0,000 0,000 0,012 40 °C

90 %RH

mass gain (%)

0,010 0,008 0,006 0,004

0 %RH

0,002 0,000 0,012 0,000 50 °C

mass gain (%)

0,010

90 %RH

0,008 0,006 0,004

0 %RH 0,002

0,000 0,000 0,012 60 °C

90 %RH

mass gain (%)

0,010 0,008 0,006 0,004

0 %RH

0,002

90 %RH

0,000 0,012 70 °C 0,010

mass gain (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0,008 0,006 0,004

0 %RH

0,002 0,000

0

10

20

30

Time (days)

Figure 1 Sorption data for water vapor in PET at 23, 40, 50, 60 and 70 °C.


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3. RESULTS AND DISCUSSION

In the (T, RH) window of our study, the vapor sorption measurements in amorphous PET showed three qualitatively different behaviors. They are presented in Figure 2. The Figure 2a showed the different behaviors at constant RH (30 %) and different temperatures (23, 50 and 70 °C), whereas in the Figure 2b these three behaviors were presented at constant temperature (60 °C), but for variable RH steps (10, 40 and 90 %RH).

a)

0,06

b)

0,10 0,08

mt (mg)

0,04

mt (mg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0,02 A (23 °C - 30 % RH) B (50 °C - 30 % RH) C (70 °C - 30 % RH) 0,00

0

10

20

30

40

0,06 0,04 A (60 °C - 10 % RH) B (60 °C - 40 % RH) C (60 °C - 90 % RH)

0,02

50

0,00

0

10

Time (hours)

20

30

40

50

Time (hours)

Figure 2 Comparison of kinetics data recorded for different experimental conditions a) at RH constant (30 %), b) at temperature constant (60 °C) The first type, will be referred to as type A was observed for example at 23 °C/30 %RH and 60 °C/10 %RH (Figure 2a and b respectively in light grey). This is the most common sorption scheme, with a mass stabilization as a function of time. This behavior relates to the random motion of vapor molecules without interaction with the polymer. The water diffusion is faster than the relaxation of the polymer. This was expected in the case of PET at low temperature and humidity and was in agreement with Fickian-type sorption

20, 26

. This experimental data were


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adjusted to the Fick’s second law for the sorption of water in a film, as described by Crank et al. 37

:

8 1 $2 + 1 % = 1− !" #− ' 3 2 + 1 ℎ ()

In this equation (called Model 1 hereafter), mt represents the water uptake at time t, m∞ is the water uptake at equilibrium (48 h in the present case), h (m) the thickness of sample and D (m2.s-1) the Fickian diffusion coefficient. A good adjustment of the data with the Model 1 can be observed on Figure 3a, if a large enough number (about 100) is taken for n.


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a)

0,06

mt (mg)

0,04

0,02 A (23 °C - 30 % RH) Model 1 Model 2 0,00

0

10

20

30

40

50

Time (hours)

b)

0,06

mt (mg)

0,04

0,02 B (50 °C - 30 % RH) Model 1 Model 2 0,00

c)

0

10

20

30

40

50

Time (hours) 0,03

0,02

mt (mg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0,01 C (70 °C - 30 % RH) Model 1 Model 2 0,00

0

10

20

30

40

50

Time (hours)

Figure 3 Comparison between Model 1 and Model 2 with experimental data for the three different sorption kinetics, a) Type A, b) Type B, c) Type C

The type B was observed for example at 50 °C/30 %RH and 60 °C/40 %RH (Figure 2a and b respectively in dark grey). The sorption-rate curve exhibited a mass drift, and the mass equilibrium was not reached even after 48 h of exposition. In this case, not only Fickian sorption


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behavior can occur, but an additional mass uptake due to non-Fickian relaxation phenomena is observed

4, 10, 38

. This behavior has been largely described with glassy polymers in contact with

condensed vapors 23,

25, 26, 39-41

. This had also been measured for PET, also at moderated

temperature and at high relative humidity 26, 42. The non-Fickian relaxation can be associated to morphological changes within the polymer, such as strong plasticization 1-3, 22, 43 and free volume increase

26

. The plasticization is generally associated with a decrease in glass transition

temperature (Tg) 9, 10, combined with a degradation of stiffness and strength. In order to evaluate the effect water vapor within the polymer on its glass transition temperature, the Fox equation is generally used 44: - - 1 = + 4 +, +,, +,,

Where Tg (K) is the glass transition temperature of the water/polymer mixture, Tg,w (K) and Tg,p (K) are the glass transition temperatures of the water and the polymer respectively, and ww and wp are the weight fractions of the water and the polymer respectively. Langevin et al.

24

clearly showed in their work that Tg of PET films decreased with the relative humidity. A loss of 15 °C was measured by DSC (differential Scanning calorimetry) with a change from 0 to 100 % in relative humidity. Several authors associated this non-Fickian relaxation to chemical degradation of polymer by the water molecules. Popineau et al.

45, 46

, correlated non-conventional sorption of epoxy

thermosets to the hydrolysis of the ester functions

45, 46

. Similarly, Bastioli et al.

30

suggested a

hydrolytic degradation of PET, after immersion in hot water (87 °C ie above the Tg).


10

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In addition to chemical degradation of the covalent bonds, swelling was also attributed to the rupture of the weak bonds between the macromolecular chains, or by clustering due to selfhydrogen bonding when water molecules were absorbed in a polymer 12. In the first case, water diffusion increases with the segmental mobility. In the second case, water clusters are viewed to disfavor the diffusion by increasing the pathway of water vapor molecule

43

. These two

phenomena have even been described for several couples of penetrant/polymer 39, 43, 47-49.

In order to model this non-Fickian relaxation, several authors have developed mathematical models that describe these additional diffusion processes. The Langmuir model developed by Carter and Kibler 50, the “dual-stage” model

51

and the Berens and Hopfenberg

52

model are the

most used. The type B was non-Fickian, probably because of polymer swelling by clustering mechanism and plasticization 25, 26. To describe this peculiar behavior, Burgess et al.

26

used the

model of Berens and Hopfenberg 52 . Based on this formalism, a simplification of the model was proposed. The Fickian diffusion and the non-Fickian relaxation are both assumed to exist independently, and can therefore be simply combined with a linear superposition. So, a linear approximation with a characteristic parameter η was added to the Equation 5 (Model 2) to describe this non-Fickian behavior:

8 1 $2 + 1 % = 01 − !" #− '1 + 2% 5 2 + 1 ℎ ()

Where η (g.s-1) quantifies the mass drift over time. To facilitates the comparison between the different experimental conditions, η was normalized to the initial mass of the sample mdry and expressed in (µg/(gdry.s).10-3). This model, Model 2, is presented with more details in SI. Model 2


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allows following the changes with time for the entire sorption curve, unlike Model 1 (Figure 3b). Model 2 is very convenient because when applied to a material with a classical A behavior (Figure 3a), it works perfectly and simply gives a value of η close to 0.

The type C was observed for example at 70 °C/30 %RH and 60 °C/90 %RH (Figure 2a and b respectively in black). The sorption-rate curve exhibits a surprising non-monotonic behavior. Instead the mass first increased fairly rapidly for the first minutes of exposition to the new RH step, this was followed by a slow but significant decrease and a constant behavior. This bellshaped curve, with a distinct “overshoot” in the weight of the sample versus has been reproduced many times with great accuracy. It seemed reasonable that this reduction in weight measured in our sample arose from water rejection which was caused by a polymer densification. The latter may be related to the physical ageing or crystallization

30, 53, 54

. DSC experiments conducted on

our samples revealed a well-defined endotherm related to physical ageing. The latter could however also observed with A and B samples. The hypothesis of water rejection by physical ageing in the amorphous phase was thus unlikely. In contrast, PET presents towards crystallization a peculiar behavior. The initially amorphous polymer could well crystallize slowly above its Tg, which could plausibly be reached with the relative humidity 24, 44. In addition the C regime was only reached with a combination of temperature and humidity, even if a lower temperature could be compensated to some extend by a larger RH. It is thus suggested that this third behavior in the sorption mechanism is a crystallization favored by hydric plasticization of the amorphous phase. DSC measurements cannot unfortunately directly confirm this cold crystallization, the amplitude of the endotherm falls within the uncertainty of the apparatus. Some plasticization was however noticed with the samples C for which cold crystallization


12

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started 5 °C below that of the other samples A and B (at 60 and 70°C under water vapor). The water-induced crystallization process is favored by liquid as compared to gas water sorption. For the C type, both Models 1 and 2 were not adapted to follow the non-monotonous behavior with time (Figure 3c). Nevertheless Model 2 should overall be preferred to adjust the water sorption isotherm because it describes both the Fickian and swelling phenomena.

The type of sorption (A, B, or C) can be relatively straightforward determined with a visual examination of the sorption curves. Figure 4 shows the mass gain and the relative humidity increments obtained during water vapor sorption measurements in amorphous PET at 23, 40 and 70 °C were represented (the mass uptake for 50 and 60 °C are presented in SI). The mass gain m is defined by the ratio of the difference between wet and dry mass (m48h and mdry respectively) to mass dry matter: =

− 456 6 456

The identification of the three different behaviors was represented on the graphs showing the mass uptake curves, with the gray scale code used previously (A: light grey; B: dark grey; C: black) (Figure 4). For relative humidity ranging from 0 to 90 %, the mass uptake at 23 and 40 °C present two behaviors: A then B. The transition between the two behaviors occurs at 60 %RH at 23 °C and 50 %RH at 40 °C. The non-Fickian relaxation seems influenced by the temperature. At 70 °C, an overshoot was clearly identifiable on the sorption curves up to 30 %RH, reflecting a densification process (Type C). Between 40 and 70 %RH, a less pronounced overshoot is observed and the sorption kinetic can be identified as A type. However, the sorption mechanism was not Fickian, showing that swelling and densification compete. After 80 %RH, a very clear


13


overshoot on the mass uptakes curves was noticeable. Because of high humidity levels applied, the glass transition temperature Tg is lowered24 that promotes densification process (Type C). 3,5

23 °C

3,0

40 °C

70 °C

η (µg/gDry.s)10

-3

2,5 2,0 1,5 1,0 0,5 0,0 -0,5 1,2 bb

Mass gain (%)

1,0

60 %RH

50 %RH

A

B 0,6

C

40 %RH

0,8

B

0,4

A

80 %RH

A

C

0,2

bb 0,0 100 Relative Humidity (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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80 60 40 20 0 0

5

10

time (Days)

15

20

0

5

10

15

20

0

time (Days)

10

20

30

time (Days)

Figure 4 (down-top) Relative humidity increments, Mass gain and variation of η with the time obtained during water vapor measurements in amorphous PET at (from left to right) 23 °C, 40 °C and 70 °C. On top graphs, colors were associated with each behavior: green: Fickian – orange: swelling – red: densification – white: densification and swelling coupling. The B-type may advantageously be revealed with the determination of the non-Fickian parameter η. When η reaches measurable non-zero values (above 0.5.10-3 µg/(gdry.s) in our case) it means that the polymer swells.


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At 23 and 40 °C, the mass drift were observed from 60 and 50 %RH respectively and were in agreement with the visual examination (Figure 4 top). For these relative humidity, η became larger than the lowest measurable value estimated at 0.5.10-3 µg/(gdry.s). η further continuously increased with the relative humidity (Figure 4 top).

This indicated a larger tendency to

heterogeneous swelling from plasticization or clustering. The amplitude of time dependent swelling was also much larger at 40 °C than 23 °C. At 70 °C, below 40 %RH, η appeared mathematically negative (Figure 4 top). This results from a short time overshoot induced by the polymer densification. A negative value of η can be associated to the C behavior. From 40 %RH, η became positive and increased. This resulted from a competition between swelling and densification. Finally, above 80 %RH, η decreased and became negative again. This also corresponded to a densification (type C). In summary, positive η values could be attributed to the swelling of the polymer, whereas the negative η indicated a densification phenomenon. When this parameter is close to 0, the solubility and diffusion process are Fickian by definition. The differentiation between the three behaviors was performed with different colors on the graphs showing the variation of η parameter with time, Figure 4. Figure 5 is a map representing the η values as a function of temperature and humidity. The maximum of η in amorphous PET was observed at 50 °C and 90 %RH. Under these conditions, swelling was the fastest. This suggests that the mass equilibrium could be reached more quickly. .


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Figure 5 Variation of η with temperature and relative humidity. The dots in red materialize the different transitions identified previously using the Figure 4 and Figure S3 (in SI). The blue point materializes the transitions observed by Burgess et al.25

A classification, from the visual examination of the mass uptake curves and the study of η values for all conditions of temperature and RH tested was also represented in Figure 5 (green: Fickian sorption and diffusion; Orange: Swelling; Red: densification). Up to 50 °C, two mechanisms have been clearly distinguished: Fickian diffusion and swelling. At 60 °C, the non-Fickian relaxation started from 20 %RH and densification mechanism from 50 %RH. At 70 °C, a densification was noticed whatever the relative humidity and a combination of this latter with swelling was observed from 40 %RH. The limits of the various mechanisms observed were reported on the map (Figure 5, red dots). These boundaries appeared to follow isobars and were plotted on this graph (black line): •

The limit between Fickian behavior and swelling corresponds to 3690 Pa,

•

The transition from swelling to densification, visible with the weight overshoot, corresponded to about 11940 Pa


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The limit between Fickian and non-Fickian relaxation was also observed by Burgess et al.25 on amorphous PET. Their data point at 35 °C was added on the graph. This result confirms our classification, and the isobar as limit for these two behaviors. In Fick region, the behavior was supposed reversible by lowering relative humidity or by performing a drying sequence at a temperature below the glass transition of the polymer. Nevertheless at high temperature and humidity, where the non-Fickian relaxation (swelling) and/or densification can occurred, morphological changes in the polymer can be certainly irreversible by an increase/decrease of relative humidity25. It would now be of great interest to try and understand the kinetic and non-equilibrium aspect of these transitions by determining their time dependency and sensitivity to hydrothermal history.

Diffusion coefficients were determined for each temperature/RH couple studied (Figure 6).

1E-11

D (m²/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E-12

23 °C 50 °C 70 °C

1E-13

0

40°C 60 °C

10 20 30 40 50 60 70 80 90 100

RH (%)

Figure 6 Water diffusion coefficients in PET obtained with Model 2 (after correction of swelling) as a function to the relative humidity for each temperature studied.


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The weak increase of D for low relative humidity at 23, 40, 50 °C can be explain by the typical dual-mode behavior

26

. The decreases observed for some couple temperature/RH (for example

60 °C / 60 %RH) can be explain by a small difference between the experimental data and fitting. However, these low variations can be neglected. Then, the coefficient of Fickian diffusion D seem not depend on the relative humidity, regardless of the temperature. It was thus decided to define D as the average of the values obtained over the entire range of relative humidity (

Table 1). In the literature, authors show that phenomena of plasticization and clustering can induce respectively an increase or a decrease of D with the relative humidity 26, 39. In our study, it seems that these structural modifications have little impact on diffusion coefficient.

Table 1. Sorption and Diffusion values for amorphous PET T(°C)

RH range

D

kD

C’H

b

(m2.s-1)

(cm3(STD).cm3(Poly mer).Pa-1)

(cm3(STD).cm3(Polyme r))

(atm1 )

(±0.1 10-12)

(±0.1 10-3) 23

0-90

6.1.10-13

4.8.10-3

0.82

91.8

40

0-90

1.5.10-12

1.7.10-3

0.39

91.8

50

0-90

2.6.10-12

1.1.10-3

0.22

91.8

60

0-50

3.6.10-12

0.7.10-3

70

0-30

8.0.10-12

0.5.10-3


18

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Figure 7 represents the absorption isotherms for all temperatures studied. As expected, we can note that the non-Fickian relaxation behavior leads to a drift of the linear variation of the concentration with relative humidity (generally observed for Henry law). C exp (cm3(STP).cm-3(Polymer))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25 20 15

35 °C (Data Burgess et al. (25) 23 °C 40°C 50 °C 60 °C 70 °C

10 5 0

0 10 20 30 40 50 60 70 80 90 100

RH (%)

Figure 7 Absorption isotherm of the different temperature studied (23, 40, 50, 60 and 70 °C).

Several mathematical models exist to describe water sorption isotherm and to determine the water sorption properties and possible interactions between water molecules and materials. Nevertheless they are limited in the fitting of the experimental data.


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Cexp

10

-3

a)

3

5

0 0,0

0,2

0,12

weight gain (mg)

b)

0,10

0,4 0,6 p/p0

0,8

1,0

0,6

0,8

1,0

0,6

0,8

1,0

m (48h) exp m (48h) cor

0,08 0,06 0,04 0,0

0,2

0,4

p/p0 15

Cexp Ccor

10

-3

c)

C (cm (STP).cm (Polymer))

5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C (cm (STP).cm (Polymer))


0 0,0

0,2

0,4

p/p0

Figure 8 a) Experimental water vapor sorption isotherm of amorphous PET at 40 °C – solid line: guideline for the behavior, b) Experimental mass gain of sample (m48h) and calculated mass stem from Fickian sorption (m48h,cor) , c)Experimental data and correction with Model 2 of water vapor sorption isotherm of amorphous PET at 40 °C . Solid line: Dual Mode model


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The experimental water vapor sorption isotherm at 40 °C (Figure 8a) shows three distinct area. A concavity can be observed in low activity (a < 0.1). It can be attributed to a Langmuir mode sorption. Water molecules occupied specific sites in the polymer (microvoids) and a predominance of the penetrant-polymer interactions occurs. Between 0.1 and 0.5, a simple linear relation between the water concentration in polymer and the water activity was noticed. Then, the system water/polymer follows the Henry’s law. The gas is dispersed randomly in the matrix, which favors polymer/polymer interactions. At high activity (a > 0.5) distinct upturns occurred. This positive curve is assigned to swelling of the polymer induced plasticization. This sorption isotherm was in agreement with the previous observation, i.e. with the mass drift of the sorptionrate curve and the non-zero value for η parameter (Figure 4 top at 40 °C) from 50 %RH (whether a 0.5 activity). Some study on PET exhibit the same behavior behavior is typical of water sorption in hydrophilic materials

57

26, 28, 29, 55, 56

. This

and in this case, the BET II

(Brunner, Emmet, Teller) model, which is a combination of dual mode (Langmuir sorption and Henry law) and Flory-Huggins, was considered. However, limits of Flory-Huggins model were previously demonstrated 58. This is why, Park model can be considered. This model corresponds to a multi-sorption mode, which can be dividing in three steps: (1) Langmuir sorption, (2) Henry’s law, and (3) water clustering 57. Nevertheless, at high activity, mass equilibrium was not reached and the isotherms had time dependence. For a correct interpretation of the sorption isotherm, steady state must be reach. Moreover, similar termination of sorption before achieving true equilibrium was also done by others authors

25, 26

. Berens et al.

52

considered that the

determination of the true equilibrium was “time-consuming” and the differences between the m48h and the true equilibrium are minor due to the small “extra” non-Fickian relaxation. Nevertheless, we proposed a method to describe the water sorption without the non-Fickian


21


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Page 22 of 36

behavior. From the Fickian part of Model 2, a corrected final mass m48h,cor could be determined (SI). This mass was compared with the total mass after sorption m48h (Figure 8b). m48h,cor corresponds to the mass uptake by Fick process, whereas the difference between the two masses (m48h – m48h,cor) can be associated to the swelling process. The corrected mass was relatively constant for all RH steps, which is in good agreement with the Fickian sorption/diffusion model. The latter permitted to redefine the concentration Ccor for the water sorption isotherm and was represented in Figure 8c. Then, a linear behavior between water content Ccor and relative humidity was observed over the entire humidity range (a>0.1), in contrast with the experimental data Cexp. This may confirm that the two mechanisms, Fickian sorption and swelling, are essentially independent. In addition, the swelling was found not depend on previous states. So, clustering mechanism seems to be causing the swelling, although the coefficient D appeared constant with relative humidity. Indeed, some authors

43

showed that formation of water cluster

was accompanied by a decrease in the D coefficient with vapor activity. Permeations experiments would provide confirmation of this hypothesis by a more or less constant permeability with activity 25, 26. The dual mode is used on corrected sorption isotherm to determine the sorption properties:

895 = :; +

′= > 7 1 + >

With C’H the Langmuir capacity constant (cm3(STP).cm-3(Polymer)), b the Langmuir affinity parameter (atm-1) and kD the Henry’s law solubility coefficient (cm3(STP)/(cm3(Polymer).Pa)). All parameters, reported in


22

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Table 1, exhibited an excellent agreement with the results from various studies in the literature concerning amorphous 24, 25, 59 for the Fickian behavior.

Table 1 included also sorption parameters and diffusion coefficients between 23 °C and 70 °C and for a wide range of relative humidity (0 to 90 %RH) using the Dual Mode and Model 2 respectively. The water vapor sorption isotherms (experimental and corrected) are presented in SI (Figure S4). At 23 °C, mass drift on sorption kinetics, as evidenced by η (Figure 4 top), had negligible influence on the sorption isotherm. This results from the small amplitude of swelling. The sorption isotherms at 70 °C were identical. A deviation to linearity was observed from 40 %RH and could not be corrected with Ccor. This results from the strong interrelationship between densification and swelling. Three qualitatively different behaviors have been described with very distinctive characteristics. A a common Fickian, B a second type of Fickian process accompanied by a swelling, and C a peculiar non monotonous sorption process, due to the densification of PET.

The temperature dependency of Henry solubility coefficient kD of the PET/water system was represented in Figure 9a and follows the law of Arrhenius or Van’t Hoff:

@ = @ exp D−

EF G 8 +


23


With S the solubility coefficient (in our study, the Henry solubility coefficient kD), S0 the solubility coefficient for an infinite molecular agitation (T∞ ) and ∆HS, the dissolution enthalpy of water in PET. a) -5

Launay 1999 Current study

Ln(kD)

-6

-7

-8

-9 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036 -1

1/T (K )

b) -22

Current study Launay 1990

-23

Ln(D)

-24 -25 -26 -27 -28 -29 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036 -1

1/T (K )

-3

c) 10 η (µg/gdry.s)x10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 36

50 % HR 60 % HR 70 % HR 80 % HR 90 % HR

1

0.1 2.9

3.0

3.1

3.2 -1

3.3

3.4

3.5

-3

1/T (K .10 )

Figure 9 a) Arrhenius plot of Henry solubility coefficient (kD), kD was evaluated by a linear regression for each humidity studied, the greatest uncertainty is the uncertainty on the calculation of the regression b) Arrhenius plot of diffusion coefficient, each point was an average of all


24

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diffusion coefficients obtained for different humidity steps, the uncertainty is the standard deviation of these different values c) Variation of η with temperature and relative humidity. Dash line: Arrhenius law

As ∆HS = (-41 ± 3) kJ.mol-1 was negative, a decrease in the solubility of water in PET was observed with an increasing temperature. This expressed the fact that the water had more and more difficulties in condensing in the polymer when the temperature was raised. This result was in agreement with the literature 20, 25, 60. Launay et al. 60 studied the water sorption in amorphous PET in the 0-100 °C temperature range. Their experimental data were plotted in Figure 9a. The solubility coefficient decreased with temperature and an apparent activation energy ∆HS = -28 kJ.mol-1 was measured between 0 and 80 °C. The data of Launay et al.

60

showed a

distinct change of slope after 80 °C. This temperature was very close to the glass transition temperature of PET and this indicated that the solubility process was very different in vitreous state compared to rubbery state. Different activation energy was measured between 80 and 100 °C and estimated to -45 kJ.mol-1 for this temperature range.

The dependency of D with temperature was represented in Figure 9b. Water diffusion kinetics obeyed to Arrhenius law:

$ = $ !" D−

H; G 9 +

Where D0, the diffusion coefficient for an infinite molecular agitation (T∞) and ED, the apparent activation energy of the diffusion process. As ED= (44 ± 2) kJ.mol-1 was positive, an


25


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Page 26 of 36

increase in the diffusion of water in PET was observed with an increasing temperature. The activation energy determined by Launay et al. 60 and Burgess et al.

26

, in the same range of

temperature were respectively 42 kJ.mol-1 and 46 kJ.mol-1 and were in agreement with our study. This effect may be expressed in terms of an increase in free volume directly related to the bulk expansion and hence, the diffusion process of molecules was facilitated. To conclude, the activation energies were determined considering only the Fickian diffusion. If it is clearly shown that around 70 °C polymer densification occurs, no clear effect can be observed on the activation energies. Moreover, only one domain can be distinguished, when some authors discerned two or three domains 30, 60.

Swelling depended on the relative humidity but also appeared to be a thermally activated phenomenon by following Arrhenius law (Figure 9c):

2 = J!" D−

HK G 10 +

With Eη (J.mol-1) an activation energy, B a constant, R the gas constant (J.K-1.mol-1) and T the temperature (K). The activation energy Eη appeared constant with the relative humidity and equal to 51 kJ.mol-1. This energy was of the same order of magnitude than the sorption and diffusion.

4. CONCLUSIONS Water vapor sorption in amorphous polyethylene terephthalate has been investigated with a gravimetric method in the 23-70 °C temperature range. The water sorption isotherms followed a quasi linear relation with the relative humidity at low water concentration, in agreement with


26

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Fickian-type sorption. In contrast an up-swing effect was evidenced for high relative humidity. At high activity, the water vapor curves also exhibited a mass drift, and a mass equilibrium was not to be reached. The sorption kinetics have therefore been decomposed in two parts: the first one associated with a Fickian process and more visible at short time, while an additional non Fickian process was revealed at long time. These measurement were ascribed to the swelling of the polymer by the clustering of water molecules. The model proposed by Berens and Hopfenberg

52

was simplified with a linear approximation that easily quantified the swelling

component. A third behavior was also identified at high temperature and humidity. This case is especially visible close but bellow the Tg of the PET. The variation of mass both as a function of time and relative humidity displayed a bell shape curve. This means that water was actually rejected from the amorphous polymer. This phenomena was attributed to a PET densification, but could not be clearly attributed to its complex crystallization. The three behaviors: Fick, swelling and densification, were summarized in a “phase diagram” Figure 5. It seems reasonable to believe that the position of the frontiers depend on time and hydrothermal history of the PET. This is even more important on the application standpoint, when PET is to be used in a humid environment for a long period of time. Although the Fickian parameters, kD and D, and the swelling parameters η appeared to nicely follow an Arrhenius law in the 23-70 °C temperature range, the long term behavior might lead to unexpected behaviors.

SUPPORTING INFORMATION •

Supplements on the experimental conditions and measuring methods used.

•

Details of mathematical model (Model 2) for calculating the swelling parameters.

•

Additional representation of the data for the different temperatures studies


27


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ACKNOWLEDGMENT The authors acknowledge the ANR (French National Research Agency) for his financial support of the EMMA-PIV projects n°12-VBDU-004. This work was performed within the framework of the Center of Excellence of Multifunctional Architectured Materials (CEMAM) n°AN-10-LABEX-44-01.

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TOC GRAPHIC


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Water Vapor Sorption Properties of Polyethylene Terephthalate over a

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