Solubility and interfacial tension of thermoplastic polyurethane melt in supercritical carbon dioxide and nitrogen

Accepted Manuscript Title: Solubility and interfacial tension of thermoplastic polyurethane melt in supercritical carbon dioxide and nitrogen Author: A. Primel J. F´erec G. Ausias Y. Tirel J.-M. Veill´e Y. Grohens PII: DOI: Reference:

S0896-8446(16)30480-6 http://dx.doi.org/doi:10.1016/j.supflu.2016.11.016 SUPFLU 3802

To appear in:

J. of Supercritical Fluids

Received date: Revised date: Accepted date:

22-7-2016 25-11-2016 28-11-2016

Please cite this article as: A. Primel, J. F´erec, G. Ausias, Y. Tirel, J.-M. Veill´e, Y. Grohens, Solubility and interfacial tension of thermoplastic polyurethane melt in supercritical carbon dioxide and nitrogen, (2016), http://dx.doi.org/10.1016/j.supflu.2016.11.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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*Graphical Abstract

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*Highlights

Highlights Mixtures of TPU with supercritical CO2 and N2 were investigated. S-L EOS scaling parameters of TPU, CO2 and N2 were determined. Increasing pressure at a constant temperature enhances the solubility for both SCFs.

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The solubility of CO2 is four times greater than the one of N2 in the TPU melt.

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*Manuscript Click here to view linked References

Solubility and interfacial tension of thermoplastic polyurethane melt in supercritical carbon dioxide and nitrogen A. Primela,b , J. F´ereca , G. Ausiasa,∗, Y. Tirelb , J-M. Veill´eb , Y. Grohensa a Univ.

Bretagne Sud, FRE CNRS 3744, IRDL, F-56100 Lorient, France Standard, 194 route de Lorient, 35000 Rennes, France

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Abstract

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Various industries, such as automotive and leisure, show a great interest in foaming thermoplastic polyurethane (TPU) with physical blowing agents. Hence, this study aims to investigate the effects of absorption of carbon dioxide and nitrogen by melt TPU on solubility and interfacial tension. Using a pressure-volume-temperature apparatus for high pressure and temperature combined with a magnetic suspension balance, the solubility of carbon dioxide and nitrogen in thermoplastic polyurethane melt was measured at temperatures from 190 ◦ C to 220 ◦ C and at pressures to 25 MPa. The solubility of both supercritical fluids (SCF) in the TPU melt was then compared with semiempirical data and theoretical values calculated from the Sanchez-Lacombe equations of state (S-L EOS). The surface tension of the TPU/SCF interface was measured using the axisymmetric drop shape analysis profile. It was observed that the dependency of interfacial tension on temperature at high pressures decreases because of a reduction in SCF solubility at high temperatures. The relationship between the interfacial tension and the density difference of polymer-supercritical fluid was also examined using the generalized Macleod’s equation.

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Keywords: Thermoplastic polyurethane, Solubility, Swelling ratio, Interfacial tension

1. Introduction

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In a polymer-gas mixture, solubility is the maximum amount of gas that can be dissolved in a polymer at a specific temperature and pressure. Hence, solubility data helps to determine processing conditions for applications which require a single phase solution such as blending [1], wetting [2], dispersion of particles or fibers in polymers [3] and microcellular foaming [4]. Since the 1950s, much effort has gone into the investigation of gas solubility in polymer melts. Research methods have included experimental measurements and theoretical thermodynamic calculations. Phase equilibria [5], spectrometric [6], pressure-decay [7] and gravimetric [8] methods have been widely used to measure the solubility of physical blowing agents in polymers; however, none of them could precisely determine solubility at high temperatures and pressures because of the polymer-gas mixture swelling phenomena. To accurately measure solubility, the swollen volume or density of the polymer-gas solution must be obtained either by an equation of state (EOS) prediction or through an experimental method.

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Two steps are involved in polymer foaming using physical blowing agents: nucleation [4] and cell growth [9]. Both these processes modify the foam morphology which directly impacts on its mechanical properties [10]. The interfacial tension (IFT) author. Tel.: +33 2 97 88 05 33; Fax: +33 2 97 87 45 72 Email address: [email protected] (G. Ausias)

∗ Corresponding

Preprint submitted to The Journal of Supercritical Fluids

of polymers is a key thermodynamic parameter in order to improve the foaming behavior of microcellular foams. Based on classical nucleation theory [11], the nucleation rate is related to the exponential cubic power of surface tension. A decrease of surface tension lowers the energy barrier for cell nucleation and exponentially increases the number of cells and the cell density.

Many researchers have predicted the solubility of different chemical and physical blowing agents (carbon dioxide (CO2 ), nitrogen (N2 ), hydrofluorocarbons, hydrochlorofluorocarbon, n-butane, isobutane...) in various polymers [8, 12–17]. However, apart from a few rare studies [18–20], such as those of Hossieny et al. [19], have provided butane solubility data for thermoplastic polyurethane. To our knowledge, no literature are dealing with strong solubility data as a function of temperature and pressure for CO2 , N2 and TPU material. Recently, the automotive [21] and leisure industries have shown a great interest in replacing reticulated polyurethanes foamed with a chemical blowing agent by TPU foamed with a physical blowing agent because of its attractive mechanical, energy-absorbing, thermal-insulation properties and cost. Among physical blowing agents, supercritical fluids (SCF) such as CO2 and N2 are both suitable candidates to substitute conventional chemical blowing agents like chlorofluorocarbons [22]. Therefore, a need exists to characterize the swelling and solubility at high temperatures and pressures and to determine their effects on the interfacial tension of a TPU/SCF mixture. In this study, the scaling parameters of SanchezNovember 25, 2016

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Lacombe’s [23, 24] equations of state (S-L EOS) were obtained by applying pressure-volume-temperature data of thermoplastic polyurethane, carbon dioxide and nitrogen. These parameters were essential to get the swollen volume due to the sorption of the supercritical fluid by the polymer. The correct solubilities of TPU/CO2 and TPU/N2 mixtures were determined for a wide range of temperature and pressure. The IFT of the TPU/SCF interface was measured using an axisymmetric drop shape analysis profile (ADSA-P) and the relationship between the interfacial tension and the density difference of the polymer-supercritical fluid were examined with the generalized Macleod’s equation.

and a 15 mm piston diameter with a PTFE seal. The principle of this experiment is to measure the volume of polymer V at a fixed temperature T and compressive pressure P. Pressure increases in 5 MPa increments from 5 MPa to 25 MPa and the temperature sweep was performed at 5 ◦ C·min−1 from 190 ◦ C to 230 ◦ C. Thermodynamic data (T, P, ρ) from the National Institute of Standards and Technology were used for carbon dioxide and nitrogen [25].

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2.4. Solubility measurement 2.4.1. Apparatus for solubility measurement Sorption isotherms of CO2 and N2 in TPU melts were determined gravimetrically using a magnetic suspension balance (MSB) from Rubotherm GmbH, as shown in Fig. 1.

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2. Materials and methods 2.1. Materials

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The TPU material investigated in this study is the Irogran R A87H4615 and was received in the form of pellets from the Huntsman corporation. The soft segments are made from polyesters diols. Molecular weight was characterized by size exclusion chromatography: mass average molar mass was Mw = 108.90 kg · mol−1 and the polydispersity index was found to be PDI = 1.912. This TPU has a melting temperature of 180 ◦ C, a specific gravity of 1.20, and a hardness of 80 Shore A at 23 ◦ C. Carbon dioxide (99.995 % purity) and nitrogen (99.999 % purity) were provided by Westfalen AG, Germany.

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2.2. Size exclusion chromatography

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The high performance liquid chromatography technique requires solubilizing the polymer using a solvent, in this case a tetrahydrofuran (THF). Knowing the refractive index of the formed solution, the molar mass was determined using a light detector. Firstly, the refractive index was obtained by a linear regression using standard solutions analyzed by a differential refractometer (Optilab rEX) with a pump (Shimadzu LC20AD) and a valve with a 1 mL injection loop (Rheodyne). Then, the molecular masses of the polymer were determined by a multiangle light scattering detector (Treos) with a pump (Shimadzu LC20AD), an online degasser (Shimadzu DGU-20A), a viscosimetric detector (Viscostar-II) and an ultraviolet array diode detector (Shimadzu SPD M20A). Four chromatographic columns, measuring 30 cm in length and 7.5 mm in internal diameter, containing PLgel (particle size of 5 µm) were used in series. THF was degassed using a fluoroethylene membrane and was used as the mobile phase at a flow rate of 1 mL·min−1 . The samples were dissolved in THF and were filtered through 0.45 µm pore size polytetrafluoroethylene (PTFE) filters. Measurements were performed at 23 ◦ C.

Figure 1: A schematic of the magnetic suspension balance [13].

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At the initial stage, a polymer sample was placed in the container inside the sorption chamber. The chamber was sealed, evacuated, and preheated up. Initial weight Wg(0,T ) was the balance data readout at vacuum (P ≈ 0 MPa) and temperature (T ). The compressed fluid (CO2 or N2 ) was introduced and was maintained in the sorption chamber at the desired pressure value using a syringe pump. Temperature was controlled by a heating regulator during the whole sorption process. The weight of the sample kept increasing due to gas dissolution in the polymer sample until the equilibrium state was reached. When saturation remained stable, higher pressure gas was injected in 5 MPa increments up to a total of 25 MPa in such way that equilibrium could be obtained at each pressure stage. The weight of gas dissolved in the polymer Wg was calculated using the following relation:

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Wg = Wg(P,T ) − Wg(0,T ) + ρ1 (VH + V2 + VS )

2.3. Specific volume measurement The specific volume measurements of TPU were performed using a high-pressure capillary rheometer (Goettfert Rheograph RG20) with three temperature controlled zones in the barrel (diameter 15 mm). This instrument allows PVT measurements to be taken using a specific length/internal diameter ratio (25/2)

(1)

where Wg(P,T ) is the weight data readout at the equilibrium state at each condition (P, T ), ρ1 is the gas density, V2 is the volume of the pure polymer sample at pressure P and temperature T ; VH is the volume of the sample holder (including the sample container and the coupling device) and was measured using the 2

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buoyancy method at 200 ◦ C and 20 MPa with Argon. Finally, VS is the swollen volume of the polymer-gas mixture due to the gas dissolution. By neglecting the swollen volume term in Eq. (1), the measured weight gain was treated as the apparent weight gain (Wgapp ) and was calculated using Eq. (2):

Hence, the corrected solubility, Xcor , with the buoyancy effect compensation is obtained by:

Wgapp = Wg(P,T ) − Wg(0,T ) + ρ1 (VH + V2 )

To accurate modeling, an interaction parameter, k12 , is used such as:

Xcor = Xapp +

(2)

Hence, the apparent solubility Xapp can be evaluated: (3)

(9)


12

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Xapp

Wgapp = m0

ρ1 VS m0

P∗12 = (1 − k12 ) P∗1 P∗2

(10)

The optimal interaction parameter was determined by searching for the minimum deviation between Xtheo and Xcor :

where m0 is the initial mass of the sample.

Xtheo =

ϕ 1 M1 ϕ 1 M1 + ϕ 2 M2

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2.4.2. Correction of apparent solubility As discussed previously, the total volume of the polymer-gas mixture increased due to the gas dissolution. The swollen volume, should also be determined to accurately measure the real solubility data. The theoretical prediction of thermodynamic behavior with an EOS requires some material properties such as molecular mass and PVT data for both the pure polymer and gas systems. S-L EOS were extended to a binary system in order to calculate the density ρ: ! ! 1 ρ˜ (4) P˜ = −ρ˜ 2 − T˜ ln (1 − ρ) ˜ + 1− r

(11)

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where ϕ is the molar fraction of SCF dissolved in the polymer. Then, the swollen volume can be theoretically estimated: " #  1 1 VS = 1 + Xapp + − m0 (12) ρ12 ρ2 2.5. Interfacial tension measurement

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The ADSA-P technique was used to measure the surface tension of TPU at a different range of pressure and temperature. A schematic of the experimental set-up is shown in Fig. 2.

∗ ; R

r=

ρ˜ =

ρ ρ∗

M P∗ R T ∗ ρ∗

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T∗ =

T T˜ = ∗ ; T

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P P˜ = ∗ ; P

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In the above expression, r is the number of lattice sites occu˜ T˜ and ρ˜ are pied by the chain length of polymer molecules. P, the reduced parameters obtained from the following characteristic parameters P∗ , T ∗ and ρ∗ such as:

(5) (6)

where M is the molecular weight,  ∗ is the total interaction energy per mer [23] and R is the gas constant (i.e., 8.314 J · mol−1 · K−1 ). The gas solubility in the polymer can be calculated using the phase equilibrium theory, µG1 = µ1P , where µG1 is the chemical potential of the gas in the gas phase and µ1P is the chemical potential of gas in the polymer-gas mixture phase. The S-L EOS (Eq. (4)) were used to determine µG1 and µ1P :

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Figure 2: A schematic of the experimental device used to measure interfacial tension [30].

" ! # P˜ 1 1 1 ρ˜ 1 µG1 = r1 RT − + + − 1 ln (1 − ρ˜ 1 ) + ln ρ˜ 1 ρ˜ 1 r1 T˜ 1 ρ˜ 1 T˜ 1 (7)

The polymer is introduced with a hydraulic system consisting of a water filled hand pump and a cylindrical supply tank with a hydraulically driven piston in a capillary tip until a liquid drop of polymer is hanging. A commercial camera recorded the drop shapes through a window with a diameter of 18 mm. Heating of the chamber is carried out electrically and is controlled using two thermocouples, one inside the chamber and another one outside touching the wall. IFT was evaluated according to the Young-Laplace equation (Eq. (13)). During posterior video image processing, this equation may be applied directly by numerically solving a set of corresponding differential equations

  ! P∗ + P∗2 − 2P∗12   r1  µ1P = RT ln Φ1 + Φ2 1 − + ρr ˜ 1 Φ22 1 r2 P∗1 T˜ 1 " ! # ρ˜ 1 P˜ 1 1 1 + r1 RT − + + − 1 ln (1 − ρ˜ 1 ) + ln ρ˜ 1 (8) ρ˜ 1 r1 T˜ 1 ρ˜ 1 T˜ 1 where Φ is the reduced volume fraction, subscript 1, 2 and 12 refer to a SCF, polymer and polymer-SCF mixture respectively. 3

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CO2 T (K) 208.9 + 0.459 T + 7.56 × 10−4 T 2 269.5 328.1 369.1 338.7 353.2

ρ∗ (g · cm−3 ) 1.5800 1.5800 1.4260 1.2530 1.4141 1.2395

MSD (%) 11.00 8.49 1.64 2.03 0.22 0.07

ρ∗ (g · cm−3 ) 0.8034 0.8020

MSD (%) 0.13 0.03

N2 ∗

∗

P (MPa) 103.6 103.3

T (K) 159.0 160.2

Irogran R A87H4615 ∗

ρ∗ (g · cm−3 ) 1.2102

∗

T (K) 785.5

MSD (%) 0.02

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P (MPa) 564.4

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P (MPa) 720.3 720.3 464.3 341.2 329.1 329.1

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∗

Reference [26] [14] [27] [17] [28] This work

Reference [29] This work

Reference This work

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Table 1: S-L EOS scaling parameters for CO2 , N2 and TPU determined in a temperature range of 190 ◦ C to 230 ◦ C, and a pressure range of 5 MPa to 25 MPa

and searching for the solution that best fits the experimental drop profile by adapting the IFT. ! 1 1 ∆P = σ − (13) R1 R2 The sample was calibrated to determine the pixel size in an x and y direction, with regard to the xy stage movement. R1 and R2 are the radii of curvature and ∆P is the Laplace pressure. The density difference between both coexisting fluids is obtained using the S-L EOS. Once the deviation between the experimental and calculated profile is sufficiently low, the IFT is determined.

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3.1. S-L EOS scaling parameters Characteristic parameters P∗ , T ∗ and ρ∗ for the S-L EOS were determined for each component. Experimental data from National Institute of Standards and Technology [25] were used to determine thermodynamic behavior of carbon dioxide and nitrogen and the specific volume of thermoplastic polyurethane was obtained by PVT measurement (Fig. 3).

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This instrumentation allows other measurements to be made with a view chamber. The experimental solubility, Xexp , can be obtained from the volume expansion determined by the swelling measurement as discussed by Li et al. [31]. The swelling ratio, S w , was calculated following Eq. (14). V(T,P,teq ) (14) V(T,P,tin ) where tin and teq refer to the time at the begining of the sorption process and the time when the equilibrium state is reached, respectively. Sw =

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R Figure 3: Specific volume of Irogran A87H4615 ( ), CO2 ( ) and N2 ( ) at ◦ ◦ ◦ 190 C ( ), 200 C ( ), 210 C ( ), 220 ◦ C ( ) and 230 ◦ C ( ).

3. Results and discussions Optimal scaling parameters were calculated and compared with other values available in the literature using mean standard deviation (MSD) in a pressure range from 5 MPa to 25 MPa and a temperature range from 190 ◦ C to 230 ◦ C (Eq. (15)).

It is known that solubility as well as surface tension, in the processing range of temperature and pressure, are determining factors in order to define the processing window of microcellular foam [32] of the desired polymer. However, a few further steps are necessary before modeling the thermodynamic behavior of polymer-SCF mixtures (S-L EOS scaling parameters determination, volume swelling calculation, solubility and interfacial tension models).

! n MSD 1 X | experimental valuen − theoretical valuen | = 100 n i=1 experimental valuen (15) 4

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Results are summarized in Table 1. Differences of accuracy between characteristic parameters can be explained by the resolution algorithm (in our case the Levenberg-Marquard algorithm [33] was used) and by the ranges of pressure and temperature chosen.

swelling ratio, caused by CO2 sorption and calculated from the S-L EOS, increases linearly as a function of corrected solubility (R2 = 0.993) following Eq. (16). S w = 126.08 Xcor

(16)

3.2. Accuracy of the S-L EOS

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Based on apparent solubility data obtained through the MSB, the S-L EOS are applied to calculate the theoretical solubility and volume swelling of a TPU/CO2 mixture at 200 ◦ C. The parameters, based on the PVT behavior of the carbon dioxide and the TPU, are given in Table 1. The theoretical and corrected solubilities are compared to the experimental solubilities obtained by measuring volume swelling through a view chamber (Fig. 4.a). We observe in Fig. 4.b that the volume swelling is slightly understimated and the MSD of the S-L EOS prediction increases as a function of pressure. Nevertheless, theoretical solubility values, dependent of volume swelling, are close to the experimentally obtained solubility (MSD = 6.76 %). Mahmood et al. [8] and Hasan et al. [34] observed the same tendency by comparing EOS applicable to the PLA/CO2 mixture.

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R Figure 5: Solubility of CO2 in Irogran A87H4615 in a pressure range from 5 MPa to 25 MPa and a temperature range from 190 ◦ C to 230 ◦ C; Xcor at 190 ◦ C ( ), 200 ◦ C ( ), 210 ◦ C ( ), 220 ◦ C ( ) and 230 ◦ C ( ); Xtheo at 190 ◦ C ( ), 200 ◦ C ( ), 210 ◦ C ( ), 220 ◦ C ( ) and 230 ◦ C ( ).

Figure 4: (a) Evolution of swelling between initial and equilibrium state at R 200 ◦ C and 15.4 MPa; (b) Solubility of CO2 in Irogran A87H4615 from 3.72 MPa to 25.5 MPa at 200 ◦ C; Xapp ( ), Xtheo ( ), Xcor ( ) and Xexp ( ).

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Figure 6: 5 MPa to 190 ◦ C ( 190 ◦ C (

3.3. Solubility measurements

Figs. 5 and 6 depict the solubility data for CO2 and N2 in TPU in a pressure range from 5 to 25 MPa and a temperature range from 190 to 230 ◦ C, respectively.

R Solubility of N2 in Irogran A87H4615 in a pressure range from 25 MPa and a temperature range from 190 ◦ C to 230 ◦ C; Xcor at ), 200 ◦ C ( ), 210 ◦ C ( ), 220 ◦ C ( ) and 230 ◦ C ( ); Xtheo at ), 200 ◦ C ( ), 210 ◦ C ( ), 220 ◦ C ( ) and 230 ◦ C ( ).

In Fig. 6, solubility data of nitrogen in TPU are shown. The solubility of carbon dioxide is approximately four times greater than nitrogen in TPU. The N2 solubility behavior follows the same tendency as the CO2 , the solubility increases with pressure and decreases with increasing temperature. The swelling ratio, caused by N2 sorption, calculated from the S-L EOS increases linearly as a function of corrected solubility (R2 = 0.998) following Eq. (17).

As shown in Fig. 5, at a constant temperature, an increase in pressure increases the solubility due to the higher dissolution of gas molecules at high pressures. On the other hand, as the temperature increases, the solubility of CO2 decreases; although there is more free-volume for adsorption of gas molecules at elevated temperatures, the rate of desorption is higher. Additionally, a reduction in the polymer viscosity leads to less resistance in the retention of gas molecules in the polymer melt. The

S w = 193.53 Xcor

(17)

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This behavior is consistent with the data obtained during the sorption of N2 in polystyrene and polyethylene [15, 16]. However, it is possible to find related works with diverging sorption trends of the supercritical nitrogen for PE, PP and PS as a function of temperature [13–15].

originates from the dependency of the surface tension on the distance between the molecules: the attractive van der Waals forces decrease according to the 4th power of the intramolecular distances, an increase in fluid temperature increases the distance between molecules, and therefore density decreases [35]. Irogran R A87H4615/CO2 mixture Temperature (◦ C) 200 210 220

In Fig. 7, the variation of density of N2 , TPU/N2 mixture, the density difference between TPU/N2 mixture and surrounding N2 , and the solubility of N2 in TPU at 200 ◦ C are shown. At a constant temperature, the density of the TPU/N2 mixture does not change significantly with increasing pressure, the increase in drop volume due to N2 dissolution is compensated by an increase in mass owing due to SCF absorption. The density of the N2 increases with an increase in pressure and leads to a reduction of the density difference between two sides of the interface. The IFT exhibits no significant with temperature because at high pressure and high temperatures two concomitant effects occur : on the one hand, an increase in temperature leads to a reduction in the effective interaction between polymer and gas molecules and reduces the interfacial tension, and on the other hand, the solubility of N2 decreases for an increase in temperature. The same trends were observed for TPU/CO2 mixture, the interfacial tension of the TPU/N2 mixture is higher than the TPU/CO2 due to the density difference between carbon dioxide and nitrogen and the amount of SCF absorbed at equilibrium.

c (m3 · s−2 ) 21.770 21.759 21.757

n (-) 1.440 1.575 1.674

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3.4. Density and interfacial tension relationship

R2 (-) 0.994 0.998 0.998

Irogran R A87H4615/N2 mixture n (-) 1.161 1.287 1.360

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c (m3 · s−2 ) 26.311 26.343 26.253

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Temperature (◦ C) 200 210 220

R2 (-) 0.996 0.996 0.997

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Table 2: Generalized Macleod’s equation parameters for TPU/CO2 and TPU/N2 mixtures in a temperature range from 200 ◦ C to 220 ◦ C, and a pressure range from 5 MPa to 25 MPa

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Generalized Macleod’s equation parameters for TPU/N2 and TPU/CO2 mixtures in a wide temperature range are summarized in Table 2. The exponent n is close to 4 for many unassociated liquids of substances of low molecular weight at atmospheric pressure [35, 36]. With an increased pressure in the SCF, the Macleod exponent becomes lower because of the decreased conformational restriction at the polymer surface due to the presence of SCF molecules [37].

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The solubility of CO2 and N2 in the TPU melt was compared with semiempirical data (determined empirically by measuring the gas uptake and theoretically from swelling predictions) and theoretical values calculated from the S-L EOS. Scaling parameters for SCFs and TPU were determined using a PVT apparatus. The solubility of CO2 was approximately four times greater than the one of N2 in TPU. For both SCFs similar trends were found, at a constant temperature, an increase in pressure increases, the solubility due to higher dissolution of gas molecules at high pressures. On the other hand, at a constant pressure, as temperature increases, the solubility of CO2 decreases; the rate of desorption is higher because there is more free-volume for the adsorption of gas molecules at elevated temperatures and the reduction in the polymer viscosity leads to less resistance in the retention of gas molecules in the polymer melt.

Figure 7: Effect of pressure on density of N2 ( ) and TPU/N2 mixture ( ), on density difference between TPU/N2 mixture and surrounding N2 ( ) and on the R solubility Xcor of N2 in Irogran A87H4615 ( ) at 200 ◦ C.

The generalized Macleod’s equation is used to find the relationship between the surface tension and density difference between polymer-SCF mixture and surrounding SCF: σ = c (ρ2 − ρ1 )n

4. Conclusion In this work, we have investigated the effect of thermodynamic conditions on the interfacial tension of a TPU/SCF mixture at temperatures ranging from 190 ◦ C to 230 ◦ C and at pressures up to 25 MPa.

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(18)

where σ is the interfacial tension between the polymer and the SCF and c is a constant. n is the Macleod exponent, and ρ1 and ρ2 are the densities of the SCF and the TPU/SCF mixture, respectively. The relationship between IFT and density

At a constant temperature, an increase in pressure decreases the interfacial tension for both SCFs. The IFT exhibits no sig6

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Acknowledgments

[19]

The authors would like to thank Mrs M´elanie Legros for her support with the size exclusion chromatography measurement, located at the Institut Charles Sadron at Strasbourg, France. The authors are grateful to Dr-Ing Philip Jaeger for providing the interfacial tension measurement machine, located at Eurothechnica in Bagteheide, Germany. The authors also aknowledge Dr Jens M¨ollmer for his excellent technical assistance with the solubility measurement, located at the Institut f¨ur Nichtklassische Chemie e.V. in Leipzig, Germany.

[20]

[21] [22] [23] [24]

References

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nificant difference with temperature. The surface tension of TPU/N2 mixture is found to be higher than the TPU/CO2 due to the difference in density between carbon dioxide and nitrogen and the amount of SCF absorbed at equilibrium.

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