#
TPV Foaming by CO_{2} Extrusion: Processing and Modelling

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## Abstract

**:**

_{2}of commercial TPV and how the process influences the final morphology of the foam. Moreover, numerical modelling of the cell growth of the extrusion foaming is developed. The results show how a precise control on the saturation pressure, die geometry, temperature and nucleation can provide a homogeneous foam having a low density (<500 kg/m

^{3}). This work demonstrates that an optimum of CO

_{2}content must be determined to control the coalescence phenomenon that appears for high levels of CO

_{2}. This is explained by longer residence times in the die (time of growth under confinement) and an early nucleation (expansion on the die destabilizes the polymer flow). Finally, this work proposes a model to predict the influence of CO

_{2}on the flow (plasticizing effect) and a global model to simulate the extrusion process and foaming inside and outside the die. For well-chosen nucleation parameters, the model predicts the final mean radius of the cell foam as well as final foam density.

## 1. Introduction

_{2}or N

_{2}) is a preferred and suitable solution. Indeed, it allows the foaming of the polymer without any production of harmful gas and does not pollute the polymer [1,2].

_{2}. To generate these thermodynamic instabilities, a continuous extrusion process is widely used both on a laboratory scale and on an industrial scale. This process uses a high depressurisation rate to foam (depressurisation due to the geometry of the die). Moreover, this process has been proved to be effective on polymer blends so as to control their density while having acceptable mechanical properties [3].

_{2}leads to smaller cell sizes, explained by its high nucleation capacity, and CO

_{2}gives the lowest foam density, explained by its high solubility [6,7]. So, the CO

_{2}is the physical blowing agent (PBA) of choice (as a green blowing agent) for TPV. Based on the literature for TPV foaming, only the thermoplastic phase can expand due to the high level of crosslinking content of the EPDM phase [1,5,6].

^{3}) [8,9]. It has also been demonstrated that the temperature influences the foaming of PP [10] (and so the foaming phase of the TPV). For example, a decrease in temperature induces a decrease in cell diameter. An optimum of temperature exists depending on the polymer and its characteristic temperature (T

_{m},T

_{g}) [11].

## 2. Materials and Methods

_{2}was fed. Pressure was controlled by a Linde pump (DSD 500) which allowed for its regulation so as to reach maximal working pressure of 34.5 MPa. The precision of the pump is about 0.1 MPa and enable mass flow rate of CO

_{2}up to 5 kg/h. The depressurisation rate was set manually to 1.5 MPa/s. The saturation time was set to 45 min at 180 °C, then the foaming temperature was set and a delay of 45 min at equilibrium was set before quenching. This results in a total process time of about 2 h.

_{2}is shown in Figure 1 and the upstream CO

_{2}sealing was made through screw profile and downstream by the gear pump. Due to the configuration of the experimental device, the CO

_{2}concentration and the solubility limit are equivalent on the extruder. The CO

_{2}is injected into a partially filled area of the extruder and the pump maintains a constant saturation pressure by adjusting the CO

_{2}flow rate. Due to the small difference between the temperature on the die and on the extruder, it is assumed this is always verified (temperature on the extruder 180 °C). The schematic expected pressure profile on the extruder is demonstrated in Figure 2. The rotational speed was set at 200 rpm and the temperature of the sleeve set at 180 °C (saturation pressure).

_{2}that can be set (at 160 °C) is 5 MPa (for the die having a diameter of 1.5 mm); a lower value led to an increase of the pressure applied on the extruder beyond the safety point.

**Modelling**

**Cell growth Simulation**

_{bub}is the pressure on the bubble, P

_{sys}is the pressure outside the polymer, R is the radius of the polymer, γ is the interfacial tension of the polymer, ${\mathsf{\tau}}_{\mathrm{rr}},{\mathsf{\tau}}_{\mathsf{\theta}\mathsf{\theta}}$ are the local stress around the cell, R

_{sup}is the radius of the influenced volume.

_{g}the gas constant, c the concentration of CO

_{2}, r is the radius of the cell as a function of time.

_{sup}is fixed using experimental data as an adjustable parameter.

_{2}plasticizing effect on the rheological properties, a model developed in our previous work [16] is used as will be developed later. To model the influence of cells among themselves, a non-influence volume is assumed [13]; it is defined as the volume of polymer which is not impacted by the presence of a neighbouring cell. The concentration inside the volume of non-influence is the same at each point. As a result, the non-influence volume defines the volume where nuclei can appear. The nucleation stops when the concentration of CO

_{2}on this volume reaches a given value defined as the concentration for a nucleation rate equal to 0.01*the initial value of nucleation rate. As the nucleation stops, each cell has a specific volume to grow (influence volume of each cell). This hypothesis enables to take into account the interaction from cell to cell without taking into account coalescence.

_{2}diffusion and solubility. Since the dispersion of the EPDM/filler is fine enough regarding the characteristic volume influencing the growth (radius ≈ 10 µm, radius of EPDM nodule ≈ 500 nm), the mechanical behaviour of the polymer is assumed to be homogeneous.

**Nucleation simulation**

_{2}molecules (possible site of nucleation), ${\mathsf{\gamma}}_{\mathrm{lg}}$ is the surface tension of the polymer, M is the molar mass of the CO

_{2}, k

_{B}the Boltzmann constant, T the temperature, P

_{sys}the pressure of the system and P

_{Bub}the saturation pressure. F corresponds to the heterogeneity function.

**Plasticizing model**:

_{2}solubilization on the viscosity of the polymer (shear and extensional) is the one developed in our previous work [16]. The plasticizing influence of CO

_{2}depends on the plasticizer volumetric fraction (φ) that is derived from Daoud et al. [18] and that expresses the viscosity shift factor:

_{2}has to be calculated since the additivity of volume is not validated for gas/polymer mixtures. The equation of state of Sanchez Lacombe [19,20] (Equation (10)) is used to calculate the actual volumetric fraction of CO

_{2}(Equation (11)). The volumetric fraction that is considered is the one at pure state ${\mathsf{\phi}}_{\mathrm{i}}^{0}$.

**Foam growth resolution**

^{®}as explained in Figure 3. Then the foaming modelling uses the traditionally used equations that are specified hereafter (Equations (1)–(5)). The influence of foaming on extrusion modelling is considered using the variation of volume induced by cell growth. As a result, the foaming inside the die, through a loop, modifies the characteristic of the flow (flow rate, pressure), and thus the onset of nucleation and the behaviour inside the die. It has been evaluated that after 5 loops, a convergence to a unique solution occurs (nucleation onset on the die).

## 3. Results and Discussion

#### 3.1. Influence of CO_{2} Content on Foaming Behaviour

_{2}on the flow inside the die.

_{2}implies a nucleation upstream on the die (increase of CO

_{2}induces early nucleation) [21], combined with the decrease of viscosity induced by CO

_{2}(increase of cell growth rate). Thus, these two phenomena can induce a variation of the growth time on the matrix and create a coalescence (as we observed during batch foaming). Furthermore, this phenomenon might by emphasised due to the shear of the cell produced by the flow. In the literature, it has been demonstrated that a late nucleation induces better foam morphology [13]. This is confirmed by the SEM observations of the foam morphology as shown in Figure 5. Lower amounts of CO

_{2}lead to better foamability (no coalescence, no flow instabilities) and lower final foam densities. This is due to the onset of nucleation and the lowest growth time inside the die, which resulted in few or no coalescence. Indeed, counterintuitively the increase of CO

_{2}content does not lead to a decrease of density, demonstrating a limit to the maximal expansion of the TPV, due to the early nucleation and coalescence in the die.

^{3}), if only the PP phase has expanded, the equivalent density of the PP phase is about 250 kg/m

^{3}which can be achieved for pure PP [10]. To verify this hypothesis, TEM observations were performed on the TPV samples (Figure 5a) with the lowest density. In Figure 6a,c, the TEM image shows the presence of EPDM and PP in the cell wall which indicates the involvement of the two phases during foaming. In Figure 6, the cell wall shows a PP/EPDM blend at the surface, which indicates an expansion of the PP phase then merging with the EPDM phase described in Figure 7. The presence of multiple cells induces EPDM deformation due to the confinement induced by the cells.

_{2}. In Figure 9, the die having the highest drop of pressure and the lowest time of depressurisation enables better expansion of the TPV as demonstrated on Figure 9. It also appears that for each die, a lower value of CO

_{2}pressure enables a lower density which is directly related to a lower time of growth on the die and nucleation closer to the outlet.

#### 3.2. Numerical Modelling of Cell Growth

^{12}cell·s

^{−1}m

^{−3}, which has been proven to be the nucleation rate at the onset of nucleation for PP [7,21]). In addition, for pressures under 1.5 MPa of CO

_{2}saturation, no nucleation appears, which confirms the minimal difference of pressure of 1.5 MPa. The maximal time of growth outside the die is defined as the time of cooling outside due to the natural air convection. After a loss of 15 °C, the growth (temperature of 145 °C close to the crystallization temperature of the PP phase) is assumed to be stopped. The simulation also stops if the total initial amount of gas is used during cell growth. Using thermal modelling with only natural convection, the time of cooling outside the die was calculated at 3 s using COMSOL thermal modelling. The maximum time of growth was therefore set at 3 s.

_{Sup}was conducted and compared to the distribution of the TPV foamed (Figure 9).

_{Sup}was evaluated at 11 µm which induces a mean radius of 31 µm (Figure 10). In addition, the total number of nuclei at the end of modelling was about 1 × 10

^{13}cell/m

^{3}(calculated using J

_{hom corrected}from Equation (7)) at the end of the nucleation phase; compared to the experimental number of nuclei of 9 × 10

^{12}cell/m

^{3}, it shows accordance between modelling and experimental data. This demonstrates the ability of Park et al.’s model [3] to predict the total number of cells. In addition, the coupling with COMSOL enables a modelling of the expansion of the TPV during extrusion. The density of the modelled extrusion foaming at a saturation of 5 MPa was 510 kg·m

^{−3}(for R

_{sup}set at 11 µm) compared to the effective density of 480 kg·m

^{−3}. This demonstrates the ability of the model to predict TPV foaming. The success of the modelling depends on the value of R

_{sup}as well as on the model of nucleation chosen; in our case the modified nucleation model shows great predictability at 5 MPa.

_{Sup}is set at 11 µm and so the R

_{Sup}is then fixed for each other modelized extrusion foaming condition.

_{sup}fixed at 11 µm) demonstrated no perfect accordance between experimental and modelling: the final modelling density is about 410 kg/m

^{3}when the experimental one is about 610 kg/m

^{3}. This is explained by a longer growth time inside the die which could induce higher coalescence (which is considered as null in our model). Furthermore, a non-isotropic morphology is observed (Figure 5b) due the orientation of the cells under the flow, so that cell stability is no longer validated at 6 MPa and higher pressures, which explains the difference between experimental and modelling. From an experimental point of view, the actual limitation is the process instability itself due to the flow dominance in the die and its effect on cell growth. The experimental limitation of 6 MPa (appearance of flow instabilities) is also the divergence between experimental result and our model, which means that our model works well for stable flows. Furthermore, the influence of shear stress on the nucleation rate needs to be investigated to improve the understanding of the nucleation phase.

## 4. Conclusions

^{3}depending on saturation pressure and die temperature. However, for high values of CO

_{2}saturation pressure (p > 6 MPa), foam instabilities occur mainly due to the early nucleation inside the die and cell growth under confinement. An optimum of properties was determined that enables a density around 480 kg/m

^{3}with a homogeneous and isotropic cell morphology.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zhai, W.; Jiang, J.; Park, C.B. A review on physical foaming of thermoplastic and vulcanized elastomers. Polym. Rev.
**2022**, 62, 95–141. [Google Scholar] [CrossRef] - Banerjee, R.; Ray, S.S. Foamability and Special Applications of Microcellular Thermoplastic Polymers: A Review on Recent Advances and Future Direction. Macromol. Mater. Eng.
**2020**, 305, 2000366. [Google Scholar] [CrossRef] - Chauvet, M. Extrusion Assistee Par CO
_{2}Supercritique Appliquee au Moussage D’un Biopolymere, le Poly(Acide Lactique), Seul ou en Melange a de L’amidon: Etude Experimentale et Modelisation; Ecole des Mines d’Albi-Carmaux: Albi, France, 2017. [Google Scholar] - Kim, S.G.; Leung, S.N.; Park, C.B.; Sain, M. The effect of dispersed elastomer particle size on heterogeneous nucleation of TPO with N
_{2}foaming. Chem. Eng. Sci**2011**, 66, 3675–3686. [Google Scholar] [CrossRef] - Kim, S.G.; Park, C.B.; Kang, B.S.; Sain, M. Foamability of Thermoplastic Vulcanizates (TPVs) with Carbon Dioxide and Nitrogen. Cell. Polym.
**2006**, 25, 19–33. [Google Scholar] [CrossRef] - Kim, S.G.; Park, C.B.; Sain, M. Foamability of thermoplastic vulcanizates blown with various physical blowing agents. J. Cell Plast.
**2008**, 44, 53–67. [Google Scholar] [CrossRef] - Taki, K.; Nakayama, T.; Yatsuzuka, T.; Ohshima, M. Visual Observations of Batch and Continuous Foaming Processes. J. Cell Plast.
**2003**, 39, 155–169. [Google Scholar] [CrossRef] - Spitael, P.; Macosko, C.W. Strain Hardening in Polypropylenes and Its Role in Extrusion Foaming. Polym. Eng. Sci.
**2004**, 44, 2090–2100. [Google Scholar] [CrossRef] - Xu, Z.-M.; Jiang, X.-L.; Liu, T.; Hu, G.-H.; Zhao, L.; Zhu, Z.-N.; Yuan, W.-K. Foaming of polypropylene with supercritical carbon dioxide. J. Supercrit. Fluids
**2007**, 41, 299–310. [Google Scholar] [CrossRef] - Mohebbi, A.; Mighri, F.; Ajji, A.; Rodrigue, D. Current issues and challenges in polypropylene foaming: A review. Cell Polym.
**2015**, 34, 299–337. [Google Scholar] [CrossRef] - Naguib, H.E.; Park, C.B.; Reichelt, N. Fundamental foaming mechanisms governing the volume expansion of extruded polypropylene foams. J. Appl. Polym. Sci.
**2004**, 91, 2661–2668. [Google Scholar] [CrossRef] - Arefmanesh, A.; Advani, S.G. Diffusion-induced growth of a gas bubble in a viscoelastic fluid. Rheol Acta
**1991**, 30, 274–283. [Google Scholar] [CrossRef] - Shimoda, M.; Tsujimura, I.; Tanigaki, M.; Ohshima, M. Polymeric foaming simulation for extrusion processes. J. Cell Plast.
**2001**, 37, 517–536. [Google Scholar] [CrossRef] - Azimi, H.; Jahani, D. The experimental and numerical relation between the solubility, diffusivity and bubble nucleation of supercritical CO
_{2}in Polystyrene via visual observation apparatus. J. Supercrit. Fluids**2018**, 139, 30–37. [Google Scholar] [CrossRef] - Leung, S.N.; Park, C.B.; Xu, D.; Li, H.; Fenton, R.G. Computer simulation of bubble-growth phenomena in foaming. Ind. Eng. Chem. Res.
**2006**, 45, 7823–7831. [Google Scholar] [CrossRef] - Rainglet, B.; Chalamet, Y.; Bounor-Legaré, V.; Delage, K.; Forest, C.; Cassagnau, P. Polypropylene foams under CO
_{2}batch conditions: From formulation and rheological modeling to cell-growth simulation. Polymer**2021**, 218, 123496. [Google Scholar] [CrossRef] - Leung, S.N.; Park, C.B.; Li, H. Numerical simulation of polymeric foaming processes using modified nucleation theory. Plast. Rubber Compos.
**2006**, 35, 93–100. [Google Scholar] [CrossRef] - Daoud, M.; Cotton, J.P.; Farnoux, B.; Jannink, G.; Sarma, G.; Benoit, H.; Duplessix, C.; Picot, C.; de Gennes, P.G. Solutions of Flexible Polymers. Neutron Experiments and Interpretation. Macromolecules
**1975**, 8, 804–818. [Google Scholar] [CrossRef] - Lei, Z.; Ohyabu, H.; Sato, Y.; Inomata, H.; Smith, R.L. Solubility, swelling degree and crystallinity of carbon dioxide-polypropylene system. J. Supercrit. Fluids
**2007**, 40, 452–461. [Google Scholar] [CrossRef] - Ramesh, N.S. Foam Growth in Polymers. In Foam Extrusion, 2nd ed.; Lee, S.-T., Park, C.B., Eds.; C.R.C. Press: Boca Raton, FL, USA, 2007. [Google Scholar]
- Sun, Y.; Ueda, Y.; Suganaga, H.; Haruki, M.; Kihara, S.I.; Takishima, S. Pressure drop threshold in the foaming of low-density polyethylene, polystyrene, and polypropylene using CO
_{2}and N_{2}as foaming agents. J. Supercrit. Fluids**2015**, 103, 38–47. [Google Scholar] [CrossRef]

**Figure 4.**Comparison between experimental pressure at the inlet of the die with the model pressure using FEM method (Comsol).

**Figure 5.**Foam morphology and density for TPV foam made by extrusion foaming at various value of CO

_{2}pressure (die diameter = 1.5 mm, length 7.5 mm) at 160 °C and 5 MPa (

**a**), 6 MPa (

**b**), 7 MPa (

**c**).

**Figure 6.**TEM observation of foam obtain for saturation value of 5 MPa and 160 °C (Figure 5a–c: (

**a**) 5 MPa, (

**b**) 6 MPa, (

**c**) 7 MPa). Due to the carbon black in the EPDM, the EPDM phase appears darker than PP.

**Figure 10.**Cell growth modelling on extrusion foaming process for various superior radii (die used 1 on Figure 2).

Die | Radius (mm) | Length (mm) | Drop Pressure (MPa) ^{1} | Drop Rate Pressure (MPa/s) |
---|---|---|---|---|

1 | 0.75 | 7.5 | 9.7 | 135 |

2 | 1 | 10 | 9.2 | 45 |

^{1}220 °C, without CO

_{2}.

Parameters | Value |
---|---|

Range of R_{sup} | Between 10 and 12.5 µm |

K_{H} (at 433 K) | 1.64 × 10^{−4} mol Pa/m^{3} [11] |

D (at 433 K) | 6 × 10^{−9} m^{2}/s [2] |

R_{0} | 38 nm |

Mass flow rate | 2 kg·h^{−1} |

Saturation Pressure (MPa) | Die | T (°C) | Mean Radius Experimental (µm) | Mean Modelized Radius (µm) | Experimental Density (kg/m^{3}) | Modelized Density (kg/m^{3}) | Modelized Number of Cells (Cells/m ^{3}) | Experimental Number of Cells (Cells/m ^{3}) |
---|---|---|---|---|---|---|---|---|

7 | 1 | 160 | Deformed cell | 12 | 750 | 520 | 8.5 × 10^{13} | None |

6 | 1 | 160 | Deformed cell | 26 | 610 | 410 | 1.6 × 10^{13} | None |

5 | 1 | 160 | 30 | 31 | 480 | 510 | 8 × 10^{12} | 8 × 10^{12} |

4 | 2 | 160 | 25 | 27 | 700 | 650 | 6 × 10^{12} | 5 × 10^{12} |

3 | 2 | 165 | 19 | 22 | 770 | 740 | 4 × 10^{12} | 2.5 × 10^{12} |

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## Share and Cite

**MDPI and ACS Style**

Rainglet, B.; Besognet, P.; Benoit, C.; Delage, K.; Bounor-Legaré, V.; Forest, C.; Cassagnau, P.; Chalamet, Y.
TPV Foaming by CO_{2} Extrusion: Processing and Modelling. *Polymers* **2022**, *14*, 4513.
https://doi.org/10.3390/polym14214513

**AMA Style**

Rainglet B, Besognet P, Benoit C, Delage K, Bounor-Legaré V, Forest C, Cassagnau P, Chalamet Y.
TPV Foaming by CO_{2} Extrusion: Processing and Modelling. *Polymers*. 2022; 14(21):4513.
https://doi.org/10.3390/polym14214513

**Chicago/Turabian Style**

Rainglet, Benoit, Paul Besognet, Cyril Benoit, Karim Delage, Véronique Bounor-Legaré, Charlène Forest, Philippe Cassagnau, and Yvan Chalamet.
2022. "TPV Foaming by CO_{2} Extrusion: Processing and Modelling" *Polymers* 14, no. 21: 4513.
https://doi.org/10.3390/polym14214513