**Solubility and concomitant swelling of solvent-saturated molten polymer**

In the prediction of the relevant thermo-diffuso-chemo-mechanical behaviour of polymers, sorption is the central phenomenon. Sorption is by nature complex, since the effects of fluids solubility in polymers and of the concomitant swelling of these polymers cannot be separated.

To experimentally extract reliable solubility data, the development of inventive equipments is required. In an original way, dynamic pendulum technology under pressure is used. The advanced development proposes to combine the features of the vibrating-wire viscometer

al. (2003). Presently, performing of *in-situ* observations of phase changes based on the optical properties of polymers (Magill, 1961, 2001) under pressure is the object of a research

To estimate the solubility of penetrating agents in polymers, four main approaches are currently generating various techniques and methods, namely: gravimetric techniques, oscillating techniques, pressure decay methods, and flow methods. However, with many existing experimental devices, the gain in weight of the polymer is measured whereas the associated volume change is either estimated or sometimes neglected (Hilic et al., 2000;

The determination of key thermo-mechanical parameters coupled with diffusion and chemical effects together with temperature and pressure control is not yet well established. Approaches addressing the prediction of the multifaceted thermo-diffuso-chemomechanical (TDCM) behaviour are being suggested. Constitutive equations are built within a thermomechanical framework, like the relation based on a rigorous thermodynamic approach (Boyer et al., 2007), and the proposed formalism based on as well rigorous

Modelling of polymer phase transitions with a specific thermodynamics- and thermokinetics-based approach assumes to consider the coupling between thermal, diffusion, chemical and mechanical phenomena and to develop advanced physically-based polymer laws taking into account the morphologies and associated growth. This implies a

As regards specific industrial and technological problems, from polymer formulation to polymer damage, passing by polymer processing, the conceptualization involves largely different size scales with extensive and smart experimentation to suggest and justify suitable

**3.1 Thermodynamics as a means to understand and prevent macro-scale changes** 

Thermodynamics is a useful and powerful means to understand and prevent polymer macro-scale changes and damages resulting from molten or solid material/solvent interactions. Two engineering examples are illustrative: foaming processes with hydrochlorofluorocarbons (HCFCs) as blowing agents in extrusion processes with a concern on safeguarding the ozone layer and the global climate system, Montreal Protocol (Dixon, 2011), and transport of petroleum fluids with in-service pipelines made of structural semicrystalline polymers which are then exposed to explosive fluctuating fluid pressure

In the prediction of the relevant thermo-diffuso-chemo-mechanical behaviour of polymers, sorption is the central phenomenon. Sorption is by nature complex, since the effects of fluids solubility in polymers and of the concomitant swelling of these polymers cannot be separated. To experimentally extract reliable solubility data, the development of inventive equipments is required. In an original way, dynamic pendulum technology under pressure is used. The advanced development proposes to combine the features of the vibrating-wire viscometer

**and damages resulting from molten or solid polymer/solvent interactions** 

**Solubility and concomitant swelling of solvent-saturated molten polymer** 

project developed by Boyer (Boyer et al., 2011a).

mechanical approach (Rambert et al., 2006; Baudet et al., 2009).

**3. Development and optimization of pertinent models** 

twofold decisive step, theoretical and experimental.

approximations for theoretical analyses.

(Dewimille et al., 1993).

Nalawade et al., 2006; Li et al., 2008).

$$m\_{sol} = \rho\_{\mathcal{g}} \,\,\Delta V\_{pol} + \left[ \left( \rho\_{\mathcal{B}}^2 - \alpha\_0^2 \right) \frac{4 \,\, L^2 \,\, \mathcal{R}^2 \,\, \rho\_{\mathcal{S}}}{\pi \,\, \mathcal{g}} + \rho\_{\mathcal{g}} \left( V\_{\mathcal{C}} + V\_{pol} \right) \right] \tag{1}$$

The volume of the degassed polymer is represented by *Vpol* and *<sup>g</sup>* is the density of the solvent. The other parameters are the physical characteristics of the wire, namely, 0 and *B* which represent the natural (angular) frequencies of the wire in vacuum and under pressure, respectively. And *L*, *R, <sup>s</sup>* are, respectively, the length, the radius and the density of the wire. *VC* is the volume of the polymer container.

The thermodynamics of solvent-polymer interactions can be theoretically expressed with a small number of adjustable parameters. The currently used models are the 'dual-mode' model (Vieth et al., 1976), the cubic equation of state (EOS) as Peng-Robinson (Zhong & Masuoka, 1998) or Soave-Redlich-Kwong (Orbey et al., 1998) EOSs, the lattice-fluid model of Sanchez–Lacombe equation of state (SL-EOS) (Lacombe & Sanchez, 1976; Sanchez & Lacombe, 1976) with the extended equation of Doghieri-Sarti (Doghieri & Sarti, 1996; Sarti & Doghieri, 1998), and the Statistical Associating Fluid Theory (SAFT) (Prigogine et al., 1957; Beret & Prausnitz, 1975; Behme et al., 1999).

From the state of the art, the thermodynamic SL-EOS was preferably selected to theoretically estimate the change in volume of the polymer *versus* pressures and temperatures found in **eq. (1)**. In this model, phase equilibria of pure components or solutions are determined by equating chemical potentials of a component in coexisting phases. It is based on a welldefined statistical mechanical model, which extends the basic Flory-Huggins theory (Panayiotou & Sanchez, 1991). Only one binary adjustable interaction parameter *k*12 has to be calculated by fitting the sorption data **eqs. (2-4)**. In the mixing rule appears the volume fraction of the solvent (index 1, 1) in the polymer (index 2, 2), ( <sup>1</sup> \* , <sup>1</sup> *p* \* , <sup>1</sup> *T* \* ) and ( <sup>2</sup> \* , <sup>2</sup> *p* \* , 2 *T* \* ) being the characteristic parameters of pure compounds.

$$p\ ^\ast = \phi\_1 p\ \_1 ^\ast + \phi\_2 p\ \_2 ^\ast - \phi\_1 \phi\_2 \Delta p\ ^\ast \tag{2}$$

$$T \triangleq \frac{p \ast}{\frac{\phi\_1}{T\_1} \frac{p\_1 \ast}{\ast} + \frac{\phi\_2 p\_2 \ast}{T\_2}}\tag{3}$$

The parameter *p*\* characterizes the interactions in the mixture. It is correlated with the binary adjustable parameter *k*12.

$$
\Delta p \, ^\ast = k \, \_{12} \sqrt{p\_1 \, p\_2} \, \tag{4}
$$

The mass fraction of solvent (the permeant), 1, at the thermodynamical equilibrium is calculated with **eq. (5)**.

Thermodynamics and Thermokinetics to Model Phase Transitions of Polymers

338.22 K 363.50 K 383.22 K 402.51 K

385.34 K 402.94 K

solubility in PS with SAFT is illustrated with solid lines.

**0.15**

**(a)**

**0.10**

**Solubility**

**/ gCO2.gPS-1**

**0.05**

**0**

**0.20**

**(b)**

**0.15**

**0.10**

**Solubility**

**/ gHFC-134a.gPS-1**

**0.05**

**0**

over Extended Temperature and Pressure Ranges Under Various Hydrostatic Fluids 649

**0 10 20 30 40 50 Pressure / MPa**

**0 8 16 24 Pressure / MPa**

Fig. 2. Solubility of **(a)** CO2 (critical pressure (*Pc*) of 7.375 MPa, critical temperature (*Tc*) of 304.13 K) and **(b)** HFC-134a (*Pc* of 4.056 MPa, *Tc* of 374.18 K) in PS with **(a-insert)** literature data from pressure decay measurement (Sato et al., 1996, pressure up to 20 MPa), from elongation measurement (Wissinger & Paulaitis, 1987, pressure up to 5 MPa**),** and **(b-insert)** literature data from volumetric measurement (Sato et al., 2000, pressure up to 3 MPa), from gravimetry (Wong et al., 1998, pressure up to 4 MPa**)**. The correlation of CO2 and HFC-134a

A precise experimental methodology and a mathematical development proposed by Boyer (Boyer et al., 2006b, 2007) use the thermodynamic approach of high-pressure-controlled scanning transitiometry (*P*CST) (Grolier et al., 2004; Bessières et al., 2005). The heat resulting from the polymer/solvent interactions is measured during pressurization/depressurization runs performed under isothermal scans. Several binary polymer/fluid systems with a more or less reactive pressurizing medium have been investigated with a view to illustrate the

0.06

0.03

0

0.06

0.03

0

0 10

0 3.5

$$\rho\_1 = \frac{\phi\_1}{\phi\_1 + \left(1 - \phi\_1\right) \frac{\rho\_2 \star}{\rho\_1 \star}}\tag{5}$$

Coupled with the equation of DeAngelis (DeAngelis et al., 1999), the change in volume Δ*Vpol* of the polymer is accessible via **eq. (6)**:

$$\frac{\Delta V\_{pol}}{V\_0} = \frac{1}{\tilde{\rho}\rho^\* \left(1 - \alpha\_1\right)} \frac{1}{\hat{\nu}\_2^0} \tag{6}$$

\* and are the mixture characteristic and reduced densities, respectively. <sup>0</sup> 2 ˆ is the specific volume of the pure polymer at fixed *T*, *P* and composition. The correlation with the model is done in conjunction with the optimization of the parameter *k12* that minimizes the *A*verage of *A*bsolute *D*eviations (*AAD*) between the experimental results and the results recalculated from the fit.

The critical comparison between the semi-experimental (or semi-theoretical) data of solubility and pure-experimental data available in the literature allows us to validate the consistency of the methodology of the calculations. The combination of coupled experimental and calculated data obtained from the vibrating-wire and theoretical analyses gives access to original solubility data that were not up to now available for high pressure in the literature. As an illustration in **Fig. 2.a-b** is given the solubility of carbon dioxide (CO2) and of 1,1,1,2-tetrafluoroethane (HFC-134a) in molten polystyrene (PS). HFC-134a is significantly more soluble in PS by a factor of two compared to CO2. The parameter *k*12 was estimated at 0.9232, 0.9342, 0.9140 and 0.9120 for CO2 sorption respectively at 338, 362, 383 and 402 K. For HFC-134a sorption, it was estimated at 0.9897 and 0.9912 at 385 and 402 K, respectively. The maximum of the polymer volume change was in CO2 of 13 % at 25 MPa and 338 K, 15 % at 25 MPa and 363 K, 14 % at 43 MPa and 383 K, 13 % at 44 MPa and 403 K, and in HFC-134a of 12 % at 16 MPa and 385K, 11 % at 20 MPa and 403 K. The thermodynamic behaviour of {PS-permeant} systems with temperature is comparable to a lower critical solution temperature (LCST) behaviour (Sanchez & Lacombe, 1976).

From these data, the aptitude of the thermodynamic SAFT EOS to predict the solubility of carbon dioxide and of 1,1,1,2-tetrafluoroethane (HFC-134a) in polystyrene (PS) is evaluated. The use of SAF theoretical model is rather delicate because the approach uses a reference fluid that incorporates both chain length (molecular size and shape) and molecular association. SAF Theory is then defined in terms of the residual Helmholtz energy *a*res per mole. And *a*res is represented by a sum of three intermolecular interactions, namely, segment–segment interactions, covalent chain-forming bonds among segments and site-site interactions such as hydrogen bond association. The SAFT equation satisfactorily applies for CO2 dissolved in PS with a molecular mass in weight near about 1000 g.mol-1, while it is extended to HFC-134a dissolved in PS with a low molecular mass in weight.

### **Global cubic expansion coefficient of solvent saturated polymer as thermo-diffusochemo-mechanical parameter for preferential control of solid polymer/solvent interactions**

An essential additional information to solubility quantification, in direct relation with polymer damage by dissolved gases, is the expansion coefficient of the gas saturated polymer, *i.e.*, the mechanical cubic expansion coefficient of the polymer saturated in a solvent, *pol-g-int*.

Coupled with the equation of DeAngelis (DeAngelis et al., 1999), the change in volume Δ*Vpol*

0 2 1

are the mixture characteristic and reduced densities, respectively. <sup>0</sup>

specific volume of the pure polymer at fixed *T*, *P* and composition. The correlation with the model is done in conjunction with the optimization of the parameter *k12* that minimizes the *A*verage of *A*bsolute *D*eviations (*AAD*) between the experimental results and the results

The critical comparison between the semi-experimental (or semi-theoretical) data of solubility and pure-experimental data available in the literature allows us to validate the consistency of the methodology of the calculations. The combination of coupled experimental and calculated data obtained from the vibrating-wire and theoretical analyses gives access to original solubility data that were not up to now available for high pressure in the literature. As an illustration in **Fig. 2.a-b** is given the solubility of carbon dioxide (CO2) and of 1,1,1,2-tetrafluoroethane (HFC-134a) in molten polystyrene (PS). HFC-134a is significantly more soluble in PS by a factor of two compared to CO2. The parameter *k*12 was estimated at 0.9232, 0.9342, 0.9140 and 0.9120 for CO2 sorption respectively at 338, 362, 383 and 402 K. For HFC-134a sorption, it was estimated at 0.9897 and 0.9912 at 385 and 402 K, respectively. The maximum of the polymer volume change was in CO2 of 13 % at 25 MPa and 338 K, 15 % at 25 MPa and 363 K, 14 % at 43 MPa and 383 K, 13 % at 44 MPa and 403 K, and in HFC-134a of 12 % at 16 MPa and 385K, 11 % at 20 MPa and 403 K. The thermodynamic behaviour of {PS-permeant} systems with temperature is comparable to a

lower critical solution temperature (LCST) behaviour (Sanchez & Lacombe, 1976).

extended to HFC-134a dissolved in PS with a low molecular mass in weight.

mechanical cubic expansion coefficient of the polymer saturated in a solvent,

From these data, the aptitude of the thermodynamic SAFT EOS to predict the solubility of carbon dioxide and of 1,1,1,2-tetrafluoroethane (HFC-134a) in polystyrene (PS) is evaluated. The use of SAF theoretical model is rather delicate because the approach uses a reference fluid that incorporates both chain length (molecular size and shape) and molecular association. SAF Theory is then defined in terms of the residual Helmholtz energy *a*res per mole. And *a*res is represented by a sum of three intermolecular interactions, namely, segment–segment interactions, covalent chain-forming bonds among segments and site-site interactions such as hydrogen bond association. The SAFT equation satisfactorily applies for CO2 dissolved in PS with a molecular mass in weight near about 1000 g.mol-1, while it is

**Global cubic expansion coefficient of solvent saturated polymer as thermo-diffusochemo-mechanical parameter for preferential control of solid polymer/solvent** 

An essential additional information to solubility quantification, in direct relation with polymer damage by dissolved gases, is the expansion coefficient of the gas saturated polymer, *i.e.*, the

<sup>1</sup> <sup>1</sup>

*Vpol V*

of the polymer is accessible via **eq. (6)**:

\* and

**interactions** 

recalculated from the fit.

 

\* <sup>1</sup> \*

<sup>0</sup>

 

1 1 \* 1 ˆ

1

(5)

*pol-g-int*. (6)

2 ˆ is the

<sup>2</sup> 1 1

Fig. 2. Solubility of **(a)** CO2 (critical pressure (*Pc*) of 7.375 MPa, critical temperature (*Tc*) of 304.13 K) and **(b)** HFC-134a (*Pc* of 4.056 MPa, *Tc* of 374.18 K) in PS with **(a-insert)** literature data from pressure decay measurement (Sato et al., 1996, pressure up to 20 MPa), from elongation measurement (Wissinger & Paulaitis, 1987, pressure up to 5 MPa**),** and **(b-insert)** literature data from volumetric measurement (Sato et al., 2000, pressure up to 3 MPa), from gravimetry (Wong et al., 1998, pressure up to 4 MPa**)**. The correlation of CO2 and HFC-134a solubility in PS with SAFT is illustrated with solid lines.

A precise experimental methodology and a mathematical development proposed by Boyer (Boyer et al., 2006b, 2007) use the thermodynamic approach of high-pressure-controlled scanning transitiometry (*P*CST) (Grolier et al., 2004; Bessières et al., 2005). The heat resulting from the polymer/solvent interactions is measured during pressurization/depressurization runs performed under isothermal scans. Several binary polymer/fluid systems with a more or less reactive pressurizing medium have been investigated with a view to illustrate the

Thermodynamics and Thermokinetics to Model Phase Transitions of Polymers

systems than for less condensed {MDPE-CO2} system (Boyer et al., 2007).

complete understanding of polymer behaviour in interactions with a solvent.

**patterns using preferential liquid-crystal polymer/solvent interactions** 

transitions are about 311, 339, 368 and 388 K, respectively.

interactions taking place in LC/solvent systems.

**Polymer/pressurizing fluid interactions** 

high pressure where the parameter

over Extended Temperature and Pressure Ranges Under Various Hydrostatic Fluids 651

in the PVDF chain (Flaconnèche et al., 2001). This easiness for CO2 to dissolve is observed at

With the objective to scrutinize the complex interplay of the coupled diffusive, chemical and mechanical parameters under extreme conditions of *P* and *T*, thermodynamics plays a pivotal role. Precise experimental approaches are as crucial as numerical predictions for a

**3.2 Thermodynamics as a means to understand and control nanometric scale length** 

Thermodynamics is ideally suited to obtain specific nano-scale pattern formation, for instance 'selective decoration' of arrayed polymer structure through selected additives, by controlling simultaneously the phase diagrams of fluids and of semi-crystalline polymers. The creation of hybrid metal-polymer composite materials, with a well-controlled structure organization at the nanometric scale, is of great practical interest (Grubbs, 2005; Hamley, 2009), notably for the new generation of microelectronic and optical devices. Inorganic nanoparticles possess unique size dependent properties, from electronic, optical to magnetic properties. Among them, noble gold nanoparticles (AuNPs) are prominent. Included into periodic structures, inorganic nanoparticles can potentially lead to new collective states stemming from precise positioning of the nanoparticles (Tapalin et al., 2009). When used as thin organic smart masks, block copolymers make ideal macromolecular templates. Especially, the unique microphase separated structure of asymmetric liquid-crystal (LC) diblock copolymer (BC), like PEO-*b*-PMA(Az), develops itself spontaneously by self assemblage to form PEO channels hexagonally packed (Tian et al., 2002; Watanabe et al., 2008). PEOm-*b*-PMA(Az)n amphiphilic diblock copolymer consists of hydrophilic poly(ethylene oxide) (PEO) entity and hydrophobic poly(methacrylate) (PMA) entity bearing azobenzene mesogens (Az) in the side chains, where *m* and *n* denote the degrees of polymerization of PEO and of photoisomarized molecules azobenzene moieties, respectively. By varying *m* and *n*, the size of the diameters of PEO cylinders is controlled from 5 to 10 nm while the distance between the cylinders is 10 to 30 nm. Four phase transitions during BC heating are ascribed to PEO crystal melting, PMA(Az) glass transition, liquid crystal transition from the smectic C (SmC) phase to the smectic A (SmA) phase and isotropic transition (Yoshida et al., 2004). In PEO114-*b*-PMA(Az)46, the temperatures of the

As such, for creating smart and noble polymer-metal hybrids possessing a structure in the nanometric domain, three original aspects are discussed. They include the initial thermodynamic polymer/pressure medium interaction, the modulation of the surface topology concomitantly with the swelling of the solvent-modified nano-phase-separated organization, the "decorative" particles distribution modulation. All the aspects have an eco-aware issue and they are characterized through a rigorous analysis of the specific

The isobaric temperature-controlled scanning transitiometry (*T*CST) (Grolier et al., 2004; Bessières et al., 2005) is used to investigate the phase changes via the Clapeyron's equation while the pressure is transmitted by various fluids. The enthalpy, volume and entropy

*pol-g-int* is smaller for highly condensed {PVDF-CO2}

importance of dissociating the purely hydrostatic effect from the fluid sorption over an extended pressure range.

Taking advantage of the differential mounting of the high pressure calorimetric detector and the proper use of the thermodynamic Maxwell's relation / / *<sup>T</sup> <sup>P</sup> SP VT* , a practical expression of the global cubic expansion coefficient *pol-g-int* of the saturated polymer subjected to the compressed penetrating (permeant) solvent under isothermal conditions has been established as follows by **eq. (7)**:

$$\alpha\_{pd-g-\text{int}} = \frac{\left(Q\_{\text{diff},SS} - Q\_{\text{diff},pol}\right) + V\_{SS,r}\,\alpha\_{SS}\,T\,\Delta P}{V\_{pol}\,T\,\Delta P} \tag{7}$$

*SS* is the cubic expansion coefficient of the stainless steel of which are made the cells. *Vpol* and *VSS* are the volumes of the polymer sample placed in the measuring cell and of the stainless steel (reference) sample placed in the reference cell, respectively. The stainless steel sample is identical in volume to the initial polymer sample. *Qdiff, pol* is the differential heat between the measuring cell and the reference cell. *Qdiff, SS* is the measure of the thermodynamic asymmetry of the cells. *P* is the variation of gas-pressure during a scan at constant temperature *T*.

Three quite different pressure transmitting fluids, as regards their impact on a given polymer, have been selected: *i)* mercury (Hg), inert fluid, with well-established thermomechanical coefficients inducing exclusively hydrostatic effect, *ii)* a non-polar medium nitrogen (N2) qualified as "poor" solvent, and *iii)* "chemically active" carbon dioxide (CO2) (Glasser, 2002; Nalawade et al., 2006). While maintaining the temperature constant, the independent thermodynamic variables *P* or *V* can be scanned. Optimization and reliability of the results are verified by applying fast variations of pressure (*P* jumps), pressure scans (*P* scans) and volume scans (*V* scans) during pressurization and depressurization. Additionally, taking advantage of the differential arrangement of the calorimetric detector the comparative behaviour of two different polymer samples subjected to exactly the same supercritical conditions can be documented. As such, three main and original conclusions for quantifying the thermo-diffuso-chemo-mechanical behaviour of two polymers, a polyvinylidene fluoride (PVDF) and a medium density polyethylene (MDPE) with similar volume fraction of amorphous phase, can be drawn. This includes the reversibility of the solvent sorption/desorption phenomena, the role of the solvent (the permeant) state, *i.e.*, gaseous or supercritical state, the direct thermodynamic comparison of two polymers in real conditions of use.

The reversibility of the sorption/desorption phenomena is well observed when experiments are performed at the thermodynamic equilibrium, *i.e.*, at low rate volume scans. The preferential polymer/solvent interaction, when solvent is becoming a supercritical fluid, is emphasized with respect to the competition between plasticization and hydrostatic pressure effects. In the vicinity of the critical point of the solvent, a minimum of the *pol-g-int* coefficient is observed. It corresponds to the domain of pressure where plasticization due to the solvent sorption is counterbalanced by the hydrostatic effect of the solvent. The significant influence of the 'active' supercritical CO2 is illustrated by more energetic interactions with PVDF than with MDPE at pressure below 30 MPa (Boyer et al., 2009). The hetero polymer/CO2 interactions appear stronger than the homo interactions between molecular chains. PVDF more easily dissolves CO2 than MDPE, the solubility being favoured by the presence of polar groups C-F

importance of dissociating the purely hydrostatic effect from the fluid sorption over an

Taking advantage of the differential mounting of the high pressure calorimetric detector and the proper use of the thermodynamic Maxwell's relation / / *<sup>T</sup> <sup>P</sup> SP VT* , a

polymer subjected to the compressed penetrating (permeant) solvent under isothermal

,,,

*SS* is the cubic expansion coefficient of the stainless steel of which are made the cells. *Vpol* and *VSS* are the volumes of the polymer sample placed in the measuring cell and of the stainless steel (reference) sample placed in the reference cell, respectively. The stainless steel sample is identical in volume to the initial polymer sample. *Qdiff, pol* is the differential heat between the measuring cell and the reference cell. *Qdiff, SS* is the measure of the thermodynamic asymmetry

Three quite different pressure transmitting fluids, as regards their impact on a given polymer, have been selected: *i)* mercury (Hg), inert fluid, with well-established thermomechanical coefficients inducing exclusively hydrostatic effect, *ii)* a non-polar medium nitrogen (N2) qualified as "poor" solvent, and *iii)* "chemically active" carbon dioxide (CO2) (Glasser, 2002; Nalawade et al., 2006). While maintaining the temperature constant, the independent thermodynamic variables *P* or *V* can be scanned. Optimization and reliability of the results are verified by applying fast variations of pressure (*P* jumps), pressure scans (*P* scans) and volume scans (*V* scans) during pressurization and depressurization. Additionally, taking advantage of the differential arrangement of the calorimetric detector the comparative behaviour of two different polymer samples subjected to exactly the same supercritical conditions can be documented. As such, three main and original conclusions for quantifying the thermo-diffuso-chemo-mechanical behaviour of two polymers, a polyvinylidene fluoride (PVDF) and a medium density polyethylene (MDPE) with similar volume fraction of amorphous phase, can be drawn. This includes the reversibility of the solvent sorption/desorption phenomena, the role of the solvent (the permeant) state, *i.e.*, gaseous or supercritical state, the direct thermodynamic comparison of two polymers in real

The reversibility of the sorption/desorption phenomena is well observed when experiments are performed at the thermodynamic equilibrium, *i.e.*, at low rate volume scans. The preferential polymer/solvent interaction, when solvent is becoming a supercritical fluid, is emphasized with respect to the competition between plasticization and hydrostatic pressure

observed. It corresponds to the domain of pressure where plasticization due to the solvent sorption is counterbalanced by the hydrostatic effect of the solvent. The significant influence of the 'active' supercritical CO2 is illustrated by more energetic interactions with PVDF than with MDPE at pressure below 30 MPa (Boyer et al., 2009). The hetero polymer/CO2 interactions appear stronger than the homo interactions between molecular chains. PVDF more easily dissolves CO2 than MDPE, the solubility being favoured by the presence of polar groups C-F

effects. In the vicinity of the critical point of the solvent, a minimum of the

of the cells. *P* is the variation of gas-pressure during a scan at constant temperature *T*.

*diff SS diff pol SS r SS*

*Q Q V TP V TP*

*pol*

*pol-g-int* coefficient is

(7)

*pol-g-int* of the saturated

practical expression of the global cubic expansion coefficient

conditions has been established as follows by **eq. (7)**:

*pol g*

int

extended pressure range.

conditions of use.

in the PVDF chain (Flaconnèche et al., 2001). This easiness for CO2 to dissolve is observed at high pressure where the parameter *pol-g-int* is smaller for highly condensed {PVDF-CO2} systems than for less condensed {MDPE-CO2} system (Boyer et al., 2007).

With the objective to scrutinize the complex interplay of the coupled diffusive, chemical and mechanical parameters under extreme conditions of *P* and *T*, thermodynamics plays a pivotal role. Precise experimental approaches are as crucial as numerical predictions for a complete understanding of polymer behaviour in interactions with a solvent.
