Margaux Haurat
email: margaux.haurat@u-bordeaux.fr

Thierry Tassaing

Michel Dumon

FTIR in situ measurement of swelling and CO2 sorption in acrylic polymers at high CO2 pressures

Keywords: FTIR microscopy, CO 2 foaming, PMMA, MAM, CO 2 sorption, swelling

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In the large field of porous materials, foams have been fabricated for a long time following various methods, either chemical [START_REF] Costeux | Nanocellular foams from acrylic polymers: experiments and modeling[END_REF], [START_REF] Wagner | Foamable acrylic based ink for the production of light weight parts by inkjet-based 3D printing[END_REF], or physical [START_REF] Dumon | Block copolymer-assisted microcellular supercritical CO 2 foaming of polymers and blends[END_REF], [START_REF] Bernardo | Lowdensity PMMA/MAM nanocellular polymers using low MAM contents: Production and characterization[END_REF], [START_REF] Costeux | Continuous extrusion of nanocellular foams[END_REF]. On the one hand, chemical foaming requires the use of chemical blowing agents (CBA). Once thermally degraded or thanks to a chemical reaction, this agent generates a gas responsible of the so-called chemical foaming. On the other hand, it is possible to directly inject a gas (or a supercritical fluid) in a process to create porosities by gas expansion during the depressurization. For a few years, this solution (physical foaming) has been largely studied in order to replace some traditional CBA that tend to be forbidden by REACH regulation (e.g. azodicarbonamide). Supercritical carbon dioxide (scCO 2 ) has been mostly used as an available, cheap and non-toxic physical foaming agent in many polymers [START_REF] Kiran | Supercritical fluids and polymers -The year in review -2014[END_REF], [START_REF] Tomasko | A review of CO 2 applications in the processing of polymers[END_REF], [START_REF] Okolieocha | Microcellular to nanocellular polymer foams: Progress (2004-2015) and future directions -A review[END_REF], [START_REF] Haurat | Amorphous polymers' foaming and blends with organic foaming-aid structured additives in supercritical CO 2 , a way to fabricate porous polymers from macro to nano porosities in batch or continuous processes[END_REF]. Moreover, its critical point is rather "low" (31 °C and 7.4 MPa) so it is quite easy to reach the CO 2 critical state and take advantage of the combination of gaseous and liquid properties: good diffusivity and a good solvent capability [START_REF] Sarver | Foaming of polymers with carbon dioxide -The year-in-review -2019[END_REF], [START_REF] Dubois | On the CO 2 sorption and swelling of elastomers by supercritical CO 2 as studied by in situ high pressure FTIR microscopy[END_REF].

In order to evaluate the foamability of a polymer (or a polymer blend) in presence of scCO 2 different parameters have to be evidenced : the CO 2 ability to diffuse in and out of the polymer under supercritical conditions, sorption, desorption and polymer swelling (dilatation). In this article, we will both focus on CO 2 sorption and polymer (and blends) swelling during the saturation step before foaming.

CO 2 sorption into polymers can be characterized by various methods or devices : gravimetric method [START_REF] Pantoula | Sorption and swelling in glassy polymer/carbon dioxide systems Part I. Sorption[END_REF], [START_REF] Pinto | Temperature influence and CO 2 transport in foaming processes of poly(methyl methacrylate)-block copolymer nanocellular and microcellular foams[END_REF], quartz microbalance (QCM) [START_REF] Li | Study of the anomalous sorption behavior of CO 2 into poly(methyl methacrylate) films in the cicinity of the critical pressure and temperature using a quartz crystal microbalance (QCM)[END_REF], [START_REF] Aubert | Solubility of carbon dioxide in polymers by the quartz crystal microbalance technique[END_REF], [START_REF] Zhang | Sorption and swelling of block copolymers in the presence of supercritical fluid carbon dioxide[END_REF] or magnetic suspension balance (MSB) [START_REF] Ushiki | Solubilities and diffusion coefficients of carbon dioxide and nitrogen in poly(methyl methacrylate) at high temperatures and pressures[END_REF], [START_REF] Rajendran | Simultaneous measurement of swelling and sorption in a supercritical CO 2 -poly(methyl methacrylate) system[END_REF]. All of them consist in calculating the mass variation before and after CO 2 saturation but the fast desorption of the sample induces some errors on the % mass CO 2 determination. This CO 2 uptake can also be determined with spectra recorded thanks to Fourier transform infrared (FTIR) microscopy [START_REF] Dubois | On the CO 2 sorption and swelling of elastomers by supercritical CO 2 as studied by in situ high pressure FTIR microscopy[END_REF], [START_REF] Vitoux | In situ IR spectroscopy and ab initio calculations to study polymer swelling by supercritical CO 2[END_REF], [START_REF] Guadagno | High-pressure CO 2 -expanded solvents: simultaneous measurement of CO 2 sorption and swelling of liquid polymers with in-situ sear-IR spectroscopy[END_REF], [START_REF] Champeau | In situ FTIR micro-spectroscopy to investigate polymeric fibers under supercritical carbon dioxide: CO2 sorption and swelling measurements[END_REF], [START_REF] Flichy | An ATR-IR study of poly (dimethylsiloxane) under high-pressure carbon dioxide: simultaneous measurement of sorption and swelling[END_REF]. As shown in this study, the use of a FTIR microscope set-up with a high-pressure cell, is a way to simultaneously measure swelling and CO 2 sorption at high pressures and at the desired temperatures. This in situ method provides information about the behavior of the studied materials facing the CO 2 saturation, under given conditions (P, T) selected to mimic CO 2 saturation in a foaming process. For example, in a batch process ("solid state foaming", represented by a typical temperature of 40 °C) or a continuous process ("melt foaming", represented by a typical temperature of 130 °C) -e.g. CO 2 extrusion -, foaming requires to optimize scCO 2 saturation at several pressures. In this study, swelling and CO 2 sorption with increasing P and T of acrylic polymer systems are studied inside the spectroscopic cell, mimicking different processes saturating conditions.

The final goal is to produce "nanofoams" by a continuous process namely extrusion foaming.

In acrylic systems CO 2 assisted extrusion (130 °C and 10 to 30 MPa) [START_REF] Elkovitch | Effect of supercritical carbon dioxide on PMMA/rubber and polystyrene/rubber blending: Visosity ratio and phase inversion[END_REF], [START_REF] Siripurapu | Generation of microcellular foams of PVDF and its blends using supercritical carbon dioxide in a continuous process[END_REF] generally leads (at the best) to micro cellular foams; whereas following a discontinuous process (batch foaming) in the same pressure range but considerably lower temperatures (around 40 °C), it is proved to be easier to obtain acrylic quasi nano foams [START_REF] Dumon | Block copolymer-assisted microcellular supercritical CO 2 foaming of polymers and blends[END_REF]. Our study should help enhancing and optimizing conditions of nano foaming. Foams, when reducing both cell size and density at the same time, are intended to exhibit enhancement of several properties, such as high thermal insulation [START_REF] Notario | Experimental validation of the Knudsen effect in nanocellular polymeric foams[END_REF] or high performance mechanical properties [START_REF] Li | Thermal-insulation, electrical, and mechanical properties of highly-expanded PMMA/MWCNT nanocomposite foams fabricated by supercritical CO 2 foaming[END_REF] (damping) or else useful for filtration [START_REF] Pinto | Temperature influence and CO 2 transport in foaming processes of poly(methyl methacrylate)-block copolymer nanocellular and microcellular foams[END_REF].

The material's choice is focused on an acrylic blend containing 90 wt% of poly(methyl methacrylate), PMMA and 10 wt% of a triblock copolymer poly(methyl methacrylate)-co-poly(butyl acrylate)-co-poly(methyl methacrylate), MAM (i.e. PMMA-PBA-PMMA, PBA is poly(butyl acrylate)). This additive is more CO 2 -philic than PMMA thanks to the butyl acrylate center block [START_REF] Lalande | Microdeformation mechanisms in rubber toughened PMMA and PMMA-based copolymers[END_REF], [START_REF] Ruiz | Micro and nano cellular amorphous polymers (PMMA, PS) in supercritical CO 2 assisted by nanostructured CO 2 -philic block copolymers -One step foaming process[END_REF], [START_REF] Pinto | Nanocellular CO 2 foaming of PMMA assisted by block copolymer nanostructuration[END_REF].

The neat PMMA matrix and neat MAM copolymer are also studied separately. Generally in the field of polymer foams, these three acrylic polymers are considered as good CO 2 -foamable candidates due to their good affinity with CO 2 (thanks to the presence of the carbonyl groups), in comparison with other kind of polymers [START_REF] Haurat | Amorphous polymers' foaming and blends with organic foaming-aid structured additives in supercritical CO 2 , a way to fabricate porous polymers from macro to nano porosities in batch or continuous processes[END_REF].

Thus the present paper quantifies CO 2 sorption, swelling and identifies the trends when temperature and/or pressure increase ; especially in view of optimizing the CO 2 uptake in a short time, while maximizing expansion and controlling a high cell density.

Materials and Methods

Materials

Carbon dioxide N45 (purity 99 %) was supplied by Air Liquide. Pellets of poly(methyl methacrylate) (PMMA) and MAM (poly(methyl methacrylate)-co-poly(butyl acrylate)-co-poly(methyl methacrylate) triblock copolymer were kindly supplied by Arkema (Lacq, France). Details on the initial materials can be found in literature [START_REF] Lalande | Microdeformation mechanisms in rubber toughened PMMA and PMMA-based copolymers[END_REF], [START_REF] Ruiz | Micro and nano cellular amorphous polymers (PMMA, PS) in supercritical CO 2 assisted by nanostructured CO 2 -philic block copolymers -One step foaming process[END_REF], [30][4] and are summarized in Table 1.

For the preparation of the PMMA/10 wt% MAM blend, PMMA and MAM pellets, were first dried 4 h at 80 °C. Then the blend was compounded by CANOE (Pau, France) using a corotative twin screw extruder (Labtech ∅ = 26 , = 40) with a temperature profile ranging from 250 to 230 °C at a screw speed of 300 rpm. Then, the blends were pelletized using a continuous cutting machine operating at the end of the line.

The PMMA, MAM and PMMA/10 wt% MAM thin films ( ≈ 0.5 ; ≈ 4 ; ≈ 1 ) were made by dissolving pellets in tetrahydrofuran solvent (THF) at 60 °C and evaporated overnight at 85 to 90 °C. A FTIR microscope (Perkin Elmer Spotlight 200) working in transflection mode was used to record infrared spectra of the studied materials. With this set-up it is possible to investigate the spectral range from 800 to 6500 cm -1 with a spatial resolution of 100 µm. Thanks to the microscope linked to the FTIR set-up, one can precisely focus the FTIR beam on the a specific part of the highpressure cell (either in the sample or on a mirror as shown in Figure 1).

In order to maintain the sample in an area saturated with CO 2 at high pressure, it was placed between a mirror and a sapphire window constituting the high-pressure cell as shown in Figure 1.

This cell was CO 2 powered at the desired pressure (up to 40 MPa) thanks to a stainless-steel capillary linked to a hydraulic pressurizing system. The temperature in the cell was regulated thanks to 4

cartridge heaters distributed all around the cell and was measured with 2 thermocouples respectively located close to the sample area and close to a cartridge heater (Figure 2). For each In this study the experiments were conducted at 40 °C or 130 °C and in a pressure range from 5 MPa to 30 MPa.

Experimental procedure

As shown in Figure 1, the thin polymer sample (about 0.5 mm) was centered between the two CO 2 arrivals before being fixed between a stainless-steel polished mirror and the window of the cell. Under these conditions, the CO 2 can diffuse inside the cell and saturate the studied sample.

Samples are allowed to swell on their non-constrained edges. Although in a batch configuration the swelling is possible in all 3 dimensions (3D), we emphasize that the polymers under investigation are isotropic in nature and we do not expect to have any influence on the swelling of the polymer even if the polymer can swell in only 2 dimensions in our IR microscopy configuration. This expected behavior was checked by Champeau et al. [START_REF] Champeau | In situ FTIR micro-spectroscopy to investigate polymeric fibers under supercritical carbon dioxide: CO2 sorption and swelling measurements[END_REF] on swelling and CO 2 sorption measurement in Polyethylene Oxide (PEO). The results obtained using a 2D configuration with Infrared microscopy were in a good agreement with literature data that were obtained under experimental conditions where the polymer could swell in 3D configuration. Finally, some of the results obtained in this study After sample positioning, the cell was heated up to the chosen temperature (40 °C or 130 °C). Once the temperature was reached, a first spectrum was recorded without CO 2 (red location shown in Figure 1). Then, CO 2 was injected at the desired pressure (5 -10 -20 -30 MPa). During the pressure stabilization a spectrum was recorded every 5 min to follow the CO 2 sorption in the material over time.

In this study, the equilibrium was generally reached after 30 to 90 min. At the end of the experiment, samples were taken out of the cell as transparent pieces (unfoamed) or slightly white pieces (close to the beginning of foaming when the cell was quickly depressurized). As shown in Figure 3, the CO 2 addition leads to spectra modifications. Different peaks associated with fundamental and combination modes of CO 2 can be observed at different wavenumbers (see Table 2). In order to determine the CO 2 mass uptake and swelling of our polymers and blend both CO 2 and polymers peaks were studied.

Table 2: IR spectral contributions of CO 2 in the spectral range 2000-5100 cm -1 [START_REF] Dubois | On the CO 2 sorption and swelling of elastomers by supercritical CO 2 as studied by in situ high pressure FTIR microscopy[END_REF] ν 1 : symmetric stretching mode; ν 2 : CO 2 bending mode; ν 3 : antisymmetric stretching mode For a quantitative analysis, we have selected non saturated (to avoid neither a too large absorbance, e.g. A > 1, nor too weak absorbance, e.g. A < 0.1) significant peaks associated with the polymer and the sorbed CO 2 at both 40 °C and 130 °C over a pressure range from 5 to 30 MPa. Then, these peaks were integrated from different onsets and endsets, and several areas were calculated (more details in Supporting Information). Finally, each set of values was used for the calculation of the CO 2 sorption, (mol.L -1 ), the CO 2 mass uptake (%) and the swelling, (%) (see details in paragraph below). Considering all the sources of errors associated with our methodology (baseline correction,

Peak wavenumber (cm -1 ) CO 2 contribution

2350 ν 3 3590 2ν 2 + ν 3 3695 ν 1 + ν 3 4950 ν 1 + 2ν 2 + ν 3 5030 2ν 1 + ν 3 4850 4ν 2 + ν 3
molar extinction coefficient, thickness of the sample, signal to noise ratio, spectrometer stability), we have evaluated a relative standard uncertainty of about ± 10 % on our results.

Data analysis

Polymer swelling

As proposed by Guadagno et al. [START_REF] Guadagno | High-pressure CO 2 -expanded solvents: simultaneous measurement of CO 2 sorption and swelling of liquid polymers with in-situ sear-IR spectroscopy[END_REF], and shown by Flichy et al. [START_REF] Flichy | An ATR-IR study of poly (dimethylsiloxane) under high-pressure carbon dioxide: simultaneous measurement of sorption and swelling[END_REF] , it is possible to determine polymer swelling using the absorbance of a specific band of polymer before and after exposure to CO 2 , according to the Beer-Lambert law:

= . . #(1) = . . #(2)
with and the absorbances before and after exposure to CO 2 ; the molar extinction coefficient of the polymer band (L.mol -1 .cm -1 ); the sample pathlength (cm); and the concentrations of polymer before and after exposure to CO 2 (mol.L -1 ).

If is the volume of the polymer before exposure to gas and + ∆ is the volume of the polymer after exposure to the gas, one can write:

= + ∆ #(3) 1 + ∆ = 1 + #(4)
By combining these equations (1) to (4), it is possible to determine the swelling ( ) with the following Equation ( 5) [START_REF] Flichy | An ATR-IR study of poly (dimethylsiloxane) under high-pressure carbon dioxide: simultaneous measurement of sorption and swelling[END_REF]:

= -1 #(5)
For this study, the broad profile centered at about 4250 cm -1 (combination of the C-H stretching and bending modes) have been selected to determine the swelling of both 100 % MAM, at 40 and 130 °C ; PMMA/10 wt% MAM at 40 and 130 °C and PMMA at 130 °C. The integrated absorbance was calculated with a baseline fixed at 4600-3780 cm -1 .

For the 100 % PMMA sample at 40 °C, the 4250 cm -1 centered profile was close to the saturation.

This is why we have used the broad band at about 6000 cm -1 (overtone of the C-H stretching modes) with a baseline fixed at 6260-5470 cm -1 to determine the integrated absorbance and calculate the polymer swelling. For the other samples, this band centered around 6000 cm -1 was unusable due to the too low signal strength.

CO 2 sorption

The Beer-Lambert law was applied to the CO 2 peaks in order to determine the concentration of CO 2 sorbed into the polymer. Equation ( 2) has been adapted to give CO 2 concentration in each polymer and blend in g.cm -3 :

= . × $ × 10 %& #(6)
with the absorbance of the CO 2 band; the molar extinction coefficient of the CO 2 band (L.mol -

1

.cm -1 ); the sample pathlentgh (cm) and $ = 44 '. ( %) the CO 2 molar mass.

In this study, the CO 2 band centered at 4950 cm -1 was chosen. In this case, the molar extinction coefficient considered is *+, -. /0 = 0.25 . ( %) . 1 %) [START_REF] Dubois | On the CO 2 sorption and swelling of elastomers by supercritical CO 2 as studied by in situ high pressure FTIR microscopy[END_REF], [START_REF] Champeau | In situ FTIR micro-spectroscopy to investigate polymeric fibers under supercritical carbon dioxide: CO2 sorption and swelling measurements[END_REF], [START_REF] Foltran | In situ FTIR investigation of the solubility and swelling of model epoxides in supercritical CO 2[END_REF]. The other peaks (2300; 3590; 3695; 4850 and 5030 cm -1 ) were not used because they were either saturated or too weak and produced large errors linked to the choice of baseline during the determination of both height and integrated area.

The sample thickness was evaluated thanks to spectra of neat CO 2 taken next to the polymer sample in the cell (i.e. on a mirror, orange location represented in Figure 1), at 4 different pressures (Figure 4). Indeed, by plotting the absorbance ( ) of one of the characteristic peak of CO 2 (4950 cm -1 in this study) as a function of CO 2 concentration in the cell ( ), it is possible to determine the pathlength ( ) thanks to the following Beer-Lambert equation (Equation ( 7)). Because varies with the saturation pressure and temperature conditions, its value, for each couple of conditions, will be found in the literature tables [32].

= × #(7)

12

As shown in Figure 5, it is possible to determine the pathlength by plotting the absorbance as a function of the CO 2 concentration. Indeed, the slope of the straight line is equal to . and we know *+, -. /0 = 0.25 . ( %) . 1 %) . The pathlength thus determined for each samples saturated at (P,T) is representative of the sample thickness. Same procedure was performed for all samples (Figure 3). Finally, the weight percentage of CO 2 (% mass CO 2 ) sorbed into the polymer was calculated with the following equation:

% 455 6 7 = + 8 9:; 1 + #(8)
with the concentration of CO 2 in the polymer sample (calculated following equation ( 2)); 8 9:;

the initial polymer density (g.cm -3 ) and the polymer swelling.

Results and discussion

CO 2 sorption through FTIR spectra recovery

The that can be used in CO 2 batch foaming for acrylic materials [START_REF] Dumon | Block copolymer-assisted microcellular supercritical CO 2 foaming of polymers and blends[END_REF]. In the same pressure range, a high temperature (130 °C) is representative of the conditions that can be used in CO 2 extrusion foaming for these kind of PMMA-based materials [START_REF] Siripurapu | Generation of microcellular foams of PVDF and its blends using supercritical carbon dioxide in a continuous process[END_REF].

In neat PMMA, the CO 2 concentration in the polymer sample increases with the pressure, no matter the temperature. At 40 °C and 30 MPa the PMMA sample contains 22 wt% CO 2 while at 130 °C and 30 MPa it contains 26 wt% CO 2 . These results are quite consistent with values measured by gravimetric methods, as shown in Figure 7 [12], [START_REF] Ushiki | Solubilities and diffusion coefficients of carbon dioxide and nitrogen in poly(methyl methacrylate) at high temperatures and pressures[END_REF].

In neat MAM copolymer at 40 °C, the measured CO 2 sorption values follow the same increasing trend as in PMMA but reaches a much higher value, close to 45 wt% e.g. at 40 °C and 30 MPa. It was impossible to measure the CO 2 sorption at 130°C in MAM using our experimental set-up because of the polymer flow, as previously stated.

Neat MAM or the PMMA/10 wt% MAM blend have a higher CO 2 sorption than neat PMMA in all pressure-temperature conditions because the PBA (central block of the MAM triblock copolymer) have a much higher CO 2 sorption than PMMA (PMMA chains either as homopolymer in the PMMA matrix or as lateral blocks in MAM). Therefore, the dispersion of MAM as micelles can act as "CO 2 -reservoirs" in a PMMA matrix [START_REF] Dumon | Block copolymer-assisted microcellular supercritical CO 2 foaming of polymers and blends[END_REF][29],

and will increase the cell density of our foams. In fact, the 90/10 blend has advantageously a highly nonlinear behavior, i.e. the resulting sorption is not a linear combination of the two polymers sorption. For example, swelling of the PMMA/10 wt% MAM blend may reach values close to those of 100 % MAM at low pressure. Also, the CO 2 sorption of the PMMA matrix is multiplied by 2 as soon as 10 wt% MAM is added.

In the blend (PMMA/10 wt% MAM), at a chosen temperature (40 or 130 °C), the CO 2 mass uptake logically increases with pressure, but in two different trends, one seemingly close to that of neat MAM at 40 °C, and one seemingly close to that of PMMA at 130 °C. Generally speaking, as observed in various polymers [START_REF] Tomasko | A review of CO 2 applications in the processing of polymers[END_REF], [START_REF] Dubois | On the CO 2 sorption and swelling of elastomers by supercritical CO 2 as studied by in situ high pressure FTIR microscopy[END_REF], [START_REF] Vitoux | In situ IR spectroscopy and ab initio calculations to study polymer swelling by supercritical CO 2[END_REF], the sorption curves may have different behaviors upon pressure rise. Either the pressure curve is first linear and then it is levelling off (existence of a plateau) or it exhibits a purely linear regime. Indeed Tomasko et al. [START_REF] Tomasko | A review of CO 2 applications in the processing of polymers[END_REF] have shown that depending on the pressure range, the CO 2 sorption is not always proportional to CO 2 pressure. This is due to the variations of the Henry's coefficient (> ? ) in Henry's law (Equation 9):

= > ? × @ #(9)
with the concentration of CO 2 sorbed into the polymer sample (in g.cm -3 ), > ? the Henry's coefficient (in g.cm -3 .MPa -1 ) and @ the pressure of the CO 2 (in MPa).

Indeed, at low pressure, > ? is often dependent on temperature and polymer state, and at high pressure, > ? may not be constant and becomes dependent on the CO 2 sorption.

In our case, linearity of CO 2 mass uptake (vs pressure) is observed when PMMA/CO 2 mixture is in the rubbery state (130 °C) and therefore a pseudo-Henry's law is obeyed. Even if the intercept is not 0 at 0 MPa, a Henry's coefficient is evaluated from the slope of the = B(@) curve (Figure 6). For PMMA at 130°C, k H = 5.9 10 -9 Pa -1 = 1.4 10 -5 mol.g -1 .bar -1 . Our work seems to be the first evaluation of Henry's constant by a FTIR method. This value is in very good agreement with literature values for other molten polymer/CO 2 solutions.

Polymer/CO 2 systems were already studied as pressure dependency [START_REF] Chen | Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch-water mixtures at elevated pressures[END_REF], [START_REF] Chen | Solubility and diffusivity of CO 2 in polypropylene/micro-calcium carbonate composites[END_REF], [START_REF] Md | A thermodynamic study of CO 2 sorption and thermal transition of PolyActive TM under elevated pressure[END_REF]. Chen at al.

[34] found a very similar order of magnitude (6 10 -9 Pa -1 ) for melted polypropylene in CO 2 , at 200 °C (same pressure range). Rahman et al. [START_REF] Md | A thermodynamic study of CO 2 sorption and thermal transition of PolyActive TM under elevated pressure[END_REF] found Henry's coefficients between 2 and 5 10 -5 mol.g -

1

.bar -1 in two melt CO 2 -philic diblock copolymers based on poly(ethylene glycol terephthalate) (PEGT)

and poly(butylene terephthalate) (PBT), also consistent with our FTIR-determined value of k H .

On another side, Figure 7, plotting a comparison of CO 2 sorptions in PMMA measured by various methods, shows that FTIR CO 2 -sorptions are in good agreement with values obtained following other methods. As an example, in a PMMA/MAM blend at the same (P,T) conditions, Pinto et al. [START_REF] Pinto | Temperature influence and CO 2 transport in foaming processes of poly(methyl methacrylate)-block copolymer nanocellular and microcellular foams[END_REF] measured a CO 2 uptake of 30 wt% by gravimetry (weighting the sample after batch saturation) at 40 °C and 30 MPa. However, this is a rather low value, in comparison with our FTIR-measured value of 42 wt%. In our case, we measured the CO 2 sorption in the cell during the saturation whereas they measured it after a possible desorption, once the CO 2 vessel is opened. This difference can principally explain the gap between their value and the one we measured. Another source of difference is the sample geometry and volume.

Figure 7 : CO 2 mass uptake in PMMA as a function of pressure, comparison of results obtained following various methods such as quartz crystal microbalance (QCM) [START_REF] Pinto | Temperature influence and CO 2 transport in foaming processes of poly(methyl methacrylate)-block copolymer nanocellular and microcellular foams[END_REF], [START_REF] Li | Study of the anomalous sorption behavior of CO 2 into poly(methyl methacrylate) films in the cicinity of the critical pressure and temperature using a quartz crystal microbalance (QCM)[END_REF], [START_REF] Aubert | Solubility of carbon dioxide in polymers by the quartz crystal microbalance technique[END_REF], [START_REF] Zhang | Sorption and swelling of block copolymers in the presence of supercritical fluid carbon dioxide[END_REF], microbalance [START_REF] Chen | Solubility and diffusivity of CO 2 in polypropylene/micro-calcium carbonate composites[END_REF], gravimetry [START_REF] Dubois | On the CO 2 sorption and swelling of elastomers by supercritical CO 2 as studied by in situ high pressure FTIR microscopy[END_REF], two density method (in which both swelling and CO 2 -soprtion are simultaneously measured) [START_REF] Ushiki | Solubilities and diffusion coefficients of carbon dioxide and nitrogen in poly(methyl methacrylate) at high temperatures and pressures[END_REF] or FTIR (this work, [START_REF] Md | A thermodynamic study of CO 2 sorption and thermal transition of PolyActive TM under elevated pressure[END_REF]).

CO 2 sorption through FTIR spectra recovery

While measuring the in situ CO 2 sorption, swelling was evaluated at, respectively, 40 °C and 130 °C under a pressure ranging from 5 to 30 MPa. Swelling of PMMA, MAM and PMMA/10 wt% MAM was calculated with Equation 5, analyzing the polymer peak, and plotted as a function of pressure in Figure 8.Generally speaking, the swelling ratio (S) follows globally a similar trend as solubility with increasing CO 2 pressure. For neat PMMA at 40 °C, a swelling plateau value is reached above 20 MPa with a well-defined swelling maximum of roughly 30 %. It shows that the "best" conditions before foaming are attained at a rather low pressure, i.e. there is no need to reach 30 MPa.

The situation is somehow different for PMMA at 130 °C where the state is definitely well above the plasticized T g of the polymer/CO 2 system, so that the system is able to flow, and swelling is constantly increasing.

In a similar manner, for neat MAM and a blend containing MAM, i.e. a PBA block, no matter the temperature, swelling increases constantly with the pressure and does not reach a plateau value in these conditions. This phenomenon is due to the increase in the free volume where the CO 2 can enter thanks to the mobility of the chains and their disentanglement.

Correlation between swelling and sorption

In order to evaluate a direct correlation (i.e. a linear proportional relation) between CO 2 solubility and swelling, swelling is plotted as a function of CO 2 mass uptake in Figure 9. Among studies dealing with several CO 2 /amorphous neat polymer homogeneous systems (PS, PMMA, PC,…), studied by any method, a global (not necessarily linear) correlation between swelling and sorption is always observed [START_REF] Rajendran | Simultaneous measurement of swelling and sorption in a supercritical CO 2 -poly(methyl methacrylate) system[END_REF], [START_REF] Wissinger | Swelling and sorption in polymer-CO 2 mixtures at elevated pressures[END_REF], [START_REF] Yang | Sorption and diffusion of methane and carbon dioxide in amorphous poly(alkyl acrylates): A molecular simulation study[END_REF], [START_REF] Kazarian | Specific intermolecular interaction of carbon dioxide with polymers[END_REF], [START_REF] Liu | CO 2 -Induced PMMA swelling and multiple thermodynamic property analysis using Sanchez-Lacombe EOS[END_REF], [START_REF] Fieback | New approach for simultaneous measurement of gas absorption and swelling[END_REF], [START_REF] Hossain | Correlation/prediction of sorption, swelling, and cloud points in CO 2 + polymer systems[END_REF], [START_REF] Tsioptsias | Simultaneous determination of sorption, heat of sorption, diffusion coefficient and glass transition depression in polymer-CO 2 systems[END_REF] : a concomitant increase in swelling and sorption in isothermal conditions and a concomitant decrease with temperature in isobaric conditions were observed. Figure 9 also shows this trend in our results.

However, looking at pressure dependencies (e.g. Figure 6, Figure 7, Figure 8) or at swelling-solubility evolution (Figure 9 which is a "pressure-abstracted" dependence), the tendencies are not linear and exhibit several regimes. Figure 7 represents the pressure evolution for several polymers in literature and temperatures, compared to our systems.

and Figure 8 represent only our systems. Plateau pressures, that we name P plateau onset , were evidenced between 8 to 10 MPa [START_REF] Wissinger | Swelling and sorption in polymer-CO 2 mixtures at elevated pressures[END_REF] for neat PC at 35 °C; between 8 to 10 MPa for neat PMMA at 33 °C; or between 7 to 8 MPa for neat PMMA at 30 to 35 °C [START_REF] Liu | CO 2 -Induced PMMA swelling and multiple thermodynamic property analysis using Sanchez-Lacombe EOS[END_REF]. The plateau is lost above 40 °C, where only linear trends take place for both swelling and mass uptake.

Two regimes observed in the case of pressure dependencies ("isothermal pressure regimes") were defined by Wissinger et al. [START_REF] Wissinger | Swelling and sorption in polymer-CO 2 mixtures at elevated pressures[END_REF]. Interestingly the two regimes are eligible on all the curves (S = f(P) "dilatation curve", %CO 2 = f(P), "solubility curve", S = f(%CO 2 ) "correlation curve").

Vitoux et al. [START_REF] Vitoux | In situ IR spectroscopy and ab initio calculations to study polymer swelling by supercritical CO 2[END_REF] observed a similar pressure-swelling correlation trend for other non amorphous polymers (hydroxypoly(butadiene), poly(ethylene glycol), polysiloxane). These polymers are either liquid (HPBD, PDMS) or semi crystalline (PEG). Their behavior is the following: upon CO 2 uptake, swelling is first proportional to solubility; then swelling is much "higher" than solubility.

In regime I, isothermal swelling and sorption increase first linearly up to P plateau onset , above which solublity and swelling level off. Regime I can occur at a temperature (T experiment ) for which the CO 2 /polymer system is (or may become) glassy.

For example, such a case may occur when T g of polymers (bearing polar functions or atoms) is decreased by the CO 2 interactions [START_REF] Kazarian | Specific intermolecular interaction of carbon dioxide with polymers[END_REF] leading to a glass transition temperature named T g plasti (the so called plasticization effect) lower than the experiment saturation temperature.

A plateau regime (regime I) cannot be considered as a true (linear) correlation between sorption and swelling.

In regime II, at a chosen temperature, both sorption and swelling purely linearly increase with the pressure, over a whole pressure range at a given temperature. Such a case may occur in the liquid state of the CO 2 /polymer system. These regimes are sketched on Figure 10. The existence of these different regimes is ruled by 4 main inputs: i) the polymer/CO 2 interactions, ii) the capacity of the CO 2 to move through the free volumes and iii) the physical state of a homogeneous or a heterogeneous mixture between polymer and CO 2 [START_REF] Hwang | The relationship between gas absorption and the glass transition temperature in a batch microcellular foaming process[END_REF], iv) the pressure extent that can be investigated and the maximum pressure to which experiments are carried out.

Figure 10 is an attempt to represent schematically the two regimes, plotted as % CO 2 /S = f(P) or S = f(% CO 2 ). In our work, the behavior at 40 °C lies in regime I while behavior at 130 °C lies in regime II.

Most studies found in literature [START_REF] Rajendran | Simultaneous measurement of swelling and sorption in a supercritical CO 2 -poly(methyl methacrylate) system[END_REF], [START_REF] Wissinger | Swelling and sorption in polymer-CO 2 mixtures at elevated pressures[END_REF], [START_REF] Yang | Sorption and diffusion of methane and carbon dioxide in amorphous poly(alkyl acrylates): A molecular simulation study[END_REF], [START_REF] Kazarian | Specific intermolecular interaction of carbon dioxide with polymers[END_REF], [START_REF] Liu | CO 2 -Induced PMMA swelling and multiple thermodynamic property analysis using Sanchez-Lacombe EOS[END_REF], [START_REF] Fieback | New approach for simultaneous measurement of gas absorption and swelling[END_REF], [START_REF] Hossain | Correlation/prediction of sorption, swelling, and cloud points in CO 2 + polymer systems[END_REF], [START_REF] Tsioptsias | Simultaneous determination of sorption, heat of sorption, diffusion coefficient and glass transition depression in polymer-CO 2 systems[END_REF] are limited to 10 MPa or less, which does not allow to observe a broad pressure behavior, while our experimental set up allows to go up to 30 MPa (rather high pressure).

We define P limit as the maximum pressure attained for one experiment. Parallelly one can define P g (called glass transition pressure, P g ), the 'theoretical' transition pressure at which the CO 2 /polymer system becomes rubbery (or glassy). Most literature experiments are conducted to a low maximum pressure (e.g. P limit < 5 to 6 MPa) so that P g pressure is not always attained.

More generally, as far as pressure extent is concerned, two cases arise:

P plateau onset P 1 g P 2 g P limit 1
Pressure or Solubility

Regime I: asymptotic curve (e.g. experiment at T experiment < T g plasti )

Regime II: linear curve (e.g. experiment in liquid state) Solubility or Swelling P limit 2 20 ▪ If P limit < P g , the system cannot reach P g and the free volumes are "saturated or congested" by CO 2 .

At higher pressure or temperature, enough molecular mobility is triggered and one "gets rid" of free volume effects. ▪ If P limit > P g , one can overcome the CO 2 -penetration limit. Upon an isothermal pressure rise, one can increase the penetration of CO 2 (linear regime). Besides, we can make the hypothesis that at still higher pressures (if attainable, but not reached here), the effects of swelling and sorption would counterbalance each other, i.e. the polymer chains would constrain due to isostatic pressure, preventing CO 2 inlet (leading to loss of linearity).

On the contrary, when the system comes to a liquid or liquid-like state, e.g. 130 °C, the regime is linear (CO 2 uptake follows a dissolution mode according to Henry's law). In this regime (type II), there is a true swelling-solubility correlation.

A thermodynamic theoretical analysis is provided by Liu et al. [START_REF] Liu | CO 2 -Induced PMMA swelling and multiple thermodynamic property analysis using Sanchez-Lacombe EOS[END_REF] through the calculation and fit of an adjustable interaction parameter (named k ij ) and the application of the Sanchez-Lacombe equation of state. They calculated the values of this specific interaction parameter for the CO 2 /PMMA solution.

They showed its inversely proportional dependency with temperature, and used this only parameter to predict both solubility, swelling and T g values. Also from their study, P g is evaluated at ~ 7 MPa (33 °C, 20 wt % CO 2 ), and P g ~ 7.5 MPa (42 °C, 18 wt% CO 2 ).

In comparison to our systems, P plateau onset values are estimated from the different swelling and sorption curves, and are reported in Table 4. This table shows the existence of either a plateau pressure or of linearity in the CO 2 /polymer systems, coherent with predictions of Liu et al. [START_REF] Liu | CO 2 -Induced PMMA swelling and multiple thermodynamic property analysis using Sanchez-Lacombe EOS[END_REF].

On the other side, introducing a heterogeneous component, such as MAM or PBA block in MAM, is probably responsible for deviations from linearity in the swelling-sorption correlation (Figure 9) so that a true correlation cannot be verified.

Role of heterogeneities

If regimes I or II apply for homogeneous systems, the situation is indeed different when the CO 2 system contains a heterogeneous component, such as PBA in MAM or a MAM/PMMA blend. Here the pressure curves do not exhibit a straight forward behavior of type I or II, e.g. no plateau is well pronounced, or the onset of a plateau is not clear. Consequently, the changes in the pressure curves (swelling or sorption) are revealed as a change of slope or as a slow continuous increase.

More precisely, looking at Figure 9 (plot of swelling VS sorption), the first part of the curve (< 20-25 wt% CO 2 ) coincides with a good sorption-swelling correlation. In fact, the CO 2 -philic component (PBA, MAM) does not attract enough CO 2 to perturbate the correlation; whereas heterogeneities are responsible for perturbation at higher CO 2 solubility (> 20 %).

So in the high CO 2 -concentration region (> 25 wt% CO 2 ), a severe deviation from linearization is obvious. In this region, a true sorption-swelling correlation cannot be possible because of several reasons: different CO 2 -philicities, different mobility and dilatation states of phases. Those differences were also previously evidenced by Yang et al. [START_REF] Yang | Sorption and diffusion of methane and carbon dioxide in amorphous poly(alkyl acrylates): A molecular simulation study[END_REF] on several poly(alkyl acrylates) and in poly(butyl acrylate) in a pressure scan, especially showing differences in the evolution of void fractions in these polymers.

Conclusion

In this paper, the CO 2 uptake (solubility, % CO Furthermore, the addition of a MAM copolymer at 10 wt% in the PMMA matrix (providing an advantageous heterogeneous system) led to a significant increase of CO 2 mass uptake, from 23 % CO 2 for a neat PMMA to 42 % CO 2 for the 10 wt% MAM blend at 40 °C and 30 MPa, and of swelling (from 20 % to 90 %). MAM is confirmed as a good additive that enhances PMMA foaming in different processes (solid or liquid-like).

If both those CO 2 solubility and polymer swelling are increasing their behavior upon pressure increase is indeed different at the two temperatures in the three systems. We highlighted a purely linear increase or an increase followed by a plateau. Such a behavior corresponds to a specific regime (regime I -asymptotic-or II -linear-, presented schematically on Figure 10). Experimentally we observed either a linear correlation between swelling and sorption or a great deviation from linearity (Figure 9). The existence (or not) of a direct linear correlation is ruled by several inputs: i) the polymer/CO 2 interactions, ii) the capacity of the CO 2 to move through the free volumes and to saturate those volumes, iii) the physical state of a homogeneous or a heterogeneous mixture between polymer and CO 2 [START_REF] Hwang | The relationship between gas absorption and the glass transition temperature in a batch microcellular foaming process[END_REF], iv) the pressure extent that is investigated and the maximum pressure (P limit ) to which experiments are carried out.

For example, regime I happens if P limit < P g , the system cannot reach P g and the free volumes are "saturated or congested" by CO 2 .

On the contrary, when the system comes to a liquid or liquid-like state, e.g. 130 °C, the regime is linear (CO 2 uptake follows a dissolution mode according to Henry's law). In this regime (II), there is a true linear swelling-solubility correlation.

Such data are useful to find out the best routes towards low-density and ('and' en gras) nano porous polymer foams, given that the material be should filled with as much as possible CO 2 (at the lower possible pressure). Two chosen temperatures (40 or 130°C) are attempting to mimic a batch or an extrusion process with scCO 2 as a foaming agent.

Acknowledgments

This work was supported by the French Agence Nationale de la Recherche (ANR) [AAPG PRCE 2018 CE06 0030, 2019]; ANR is gratefully acknowledged.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to time limitations. However, the authors will try to answer questions by e-mails sent to them.

Figure 1 :

 1 Figure 1: FTIR CO 2 high-pressure cell used to measure the polymer absorbance (red arrow location) or the CO 2 absorbance (orange arrow location); a) scheme of top view, b) photograph of a sample inside the high-pressure cell

Figure 2 :

 2 Figure 2: Experimental FTIR set-up

2. 3 . Infrared spectra and data analysis 2 . 3 . 1 . 1 )Figure 3 :

 323113 Figure 3: Infrared spectra of MAM at 40 °C without CO 2 and with CO 2 at P = 5-10-20-30 MPa, showing the spectral regions used for quantitative analysis

Figure 4 :

 4 Figure 4: Infrared spectra of CO 2 at T = 40 °C and various pressures ranging from P = 6 MPa (gaseous CO 2 ) to P = 10-20-30 MPa (supercritical CO 2 )

Figure 5 : 1 )

 51 Figure 5: Integrated peak of neat CO 2 absorbance (around 4950 cm -1 ), as a function of CO 2 concentration in the polymer, at 40 °C (data obtained in the cell out of the sample, during the experiment done with the MAM sample)

Figure 6 :

 6 Figure 6: CO 2 mass uptake as function of pressure in PMMA, MAM and PMMA/10 wt% MAM at T = 40 °C and at T = 130 °C

Figure 8 :

 8 Figure 8 : Percentage of swelling of PMMA, MAM and PMMA/10 wt% MAM blend at 40 °C and 130 °C

  40 °C MAM, at 40 °C PMMA/10wt% MAM, at 40 °C PMMA, at 130 °C PMMA/10wt% MAM, at 130 °C % swelling Pressure (MPa)

Figure 9 :

 9 Figure 9: Swelling as a function of CO 2 mass uptake, in PMMA, MAM and PMMA/10 wt% MAM blend

Figure 10 :

 10 Figure 10: Schematic representation of the two regimes, represented as %CO 2 / S = f(P) or S = f(%CO 2 ); with two examples of occurrence of regime I or II, and two cases of P g (P g 1 , P g 2 ) and P limit (P limit 1 , P limit 2 ) (here experiments are carried out up to 30

Table 1 :

 1 Characteristics of the polymers used

	Material	State at room	M n	M w	Other characteristics	Density	Aspect
		temperature	(g.mol -1 )	(g.mol -1 )		(g.cm	-3 )
	PMMA V825T	glassy	43 000	83 000	use as	1.19	transparent
	clear 101	amorphous solid
					polymer matrix
		rubbery center	82 000	128 000	used as an additive	1.03*	transparent

Table 3 :

 3 Samples thicknesses calculated with equation[START_REF] Tomasko | A review of CO 2 applications in the processing of polymers[END_REF]

  (40 °C), and pressures up to 30 MPa are typically representative of the conditions

	A low temperature
		= sample at 40 °C	= sample at 130 °C
		(mm)	(mm)
	neat PMMA	0.428	0.292
	neat MAM	0.408	/
	PMMA/10 wt% MAM	0.892	0.38

in situ CO 2 sorption equilibrium values at 40 °C and 130 °C, for respectively neat PMMA, neat MAM, PMMA/10 wt% MAM blend, at 5 MPa, 10 MPa and 30 MPa, are presented in Figure

6

.

Table 4 :

 4 Existence (and pressures values) of either a plateau pressure or linearity in the sorption or swelling curves for the CO 2 systems, PMMA, MAM, PMMA/10 wt% MAM

		Neat PMMA	Neat MAM	PMMA/10 wt% MAM
		Existence and value of	Existence and value of	Existence and value of
		P	plateau onset	P	plateau onset	P	plateau onset
	Curve	Sorption=f(P) Swelling=f(P) Sorption=f(P) Swelling=f(P)	Sorption=f(P)	Swelling=f(P)
	At 40 °C	Yes		Yes	Yes		Yes (poorly	Yes	Yes
		at 10 MPa	at 15 MPa	at 10-12 MPa	defined)	at 8-10 MPa	at 20 MPa
							at 10-15
							MPa
	At 130 °C	No		No	/		/	No	No

  2 in polymer) and the polymer swelling (volume change, dilatation) in CO 2 of acrylic systems, namely poly(methyl methacrylate) homopolymer (PMMA), a triblock CO 2 -philic rubbery-core acrylic copolymer (MAM) and a PMMA/10 wt% MAM blend has been determined simultaneously using a FTIR microscope combined to a high-pressure cell. Samples were saturated with supercritical CO 2 (scCO 2 ) isothermally at either 40 °C or 130 °C up to high pressures (namely 5 MPa, 10 MPa and 30 MPa), being typical saturation temperatures of a batch scCO 2 solidstate foaming or a liquid-like state scCO 2 extrusion foaming. Pressures attained in the cell are high compared to previous works.

FTIR reveals to be a robust method for in situ simultaneous measurement of CO 2 sorption and polymer swelling. The measured values are in very good agreement with data determined by other methods in literature. Besides we provide the first coherent value of a FTIR-determined Henry's coefficient of PMMA in scCO 2 .

PMMA/10 wt% MAM (M53) at 130°C 692 Baseline (4607.180-3787.569 cm -1 )

	Pressure (MPa)	Absorbance Swelling (%)
	0.10	315.01	0
	5	280.55	12.31
	10	216.25	45.71
	20	210.20	49.91
	30	195.07	61.53
	Baseline (4767.245-3787.569 cm -1 )
	Pressure (MPa)	Absorbance Swelling (%)
	0.10	319.19	0
	5	292.09	9.28
	10	-	-
	20	214.86	48.55
	30	200.00	59.60
	Baseline (4990.951-3787.569 cm -1 )
	Pressure (MPa)	Absorbance Swelling (%)
	0.10	32..59	0
	5	295.55	9.15
	10	228.08	41.44
	20	214.40	50.47
	30	199.07	62.05
			Mean
	Pressure (MPa)	Swelling (%)	Swelling	(g.cm -3 )	% mass CO 2
	5	10.25	0.10
	10	43.57	0.44
	20	49.64	0.50	0.2	20.54
	30	61.06	0.61	0.24	24.38
	693

Supporting Information