Towards Understanding of Pore Properties of polystyrene-b-polybutadiene-b-polystyrene (SEBS) Foam Effect on Thermal Conductivity Using Numerical Analysis

Thermoplastic elastomer Polystyrene-b-polybutadiene-b-polystyrene (SEBS) foams are prepared by using carbon dioxide (CO2) as a blowing agent via a pressure quench method. During the foaming process, various pore shapes are developed inside the foam, which is influenced by several parameters such as rigidity, solubility, and diffusivity of CO2. A previous study revealed the theory of how SEBS foams may shrink due to low rigidity and high CO2 diffusivity, but empirical verification on how the final cell properties like cell shape, cell size, cell distribution, and percentage of porosity may affect the thermal conductivity of SEBS foam is challenging to represent experimentally. This is due to difficulty in preparing foam samples at different cell shapes for the same polymer, different percentages of porosity, and cell distribution while keeping the same cell size of the SEBS foam. This paper discussed how numerical analysis is employed to investigate various properties of pores such as cell shape, cell size, cell distribution, and percentage of porosity on the thermal conductivity. The simulation results are corroborated with experimental value where the reduction of thermal conductivity is observed with a higher percentage of porosity which is shown by all cell shapes foam such as spherical, ellipse, and irregular.

Numerical; Polystyrene-b-polybutadiene-b-polystyrene (SEBS); Pore; RVE.

    Polymer foams are a class of lightweight materials that possess unique properties and amazing versatility (Monie et al., 2021). They are found virtually everywhere, either in liquid or solidified form. They are widely used for packaging applications by their porous structure and superior properties of the low density of foams. The advancement of foaming technology is still in progress because the demand for foam products is widely expanded nowadays. The cell properties and cellular structure are highly dependent on their application. The essential concerns for these Polymer foams are their final foam structures and cell properties to achieve a high functionality-to-weight ratio for any polymer foam materials. To improve the thermal insulating properties of foam materials the average cell size of foam must be reduced to approach the mean free path of gas molecules in the air, as the thermal properties of air are comparable to the thermal properties of foam in a vacum (Dai et al., 2021). In biomedical applications, the requirement to be met as a bioscaffold is higher porosity, adequate pore size, structural integrity, and shape stability to the tissue defect to enable tissue regeneration during implantation (Roedel et al., 2018).
      The relationship between foam properties and its overall performance needs to be well understood by properly designing the polymer foam structure. Such an optimized cell structure design will provide superior properties by resulting in high strength, good heat transferability, and good performance to the targeted application foam. Therefore, it is vital to design the foam properties prior to preparing the foam material for any specific applications. Many studies are reported on different control strategies for controlling cell properties like selecting optimum foaming conditions (Mantaranon & Chirachanchai, 2016), utilizing nucleating agent (Chauvet et al., 2016), controlling the polymer rigidity (rheological properties) (Lee et al., 2016; Rainglet et al., 2021), performing a different method of foaming (Solbakken et al., 2021; Muayad et al., 2020), utilizing different blowing agent (Coste et al., 2020), selecting an appropriate pair of polymers in case of polymer blend foam is desired and many more methods. Zakyan et al. (2014), for example, controlled foam morphology of Polystyrene (PS) via surface chemistry, size, and concentration of nano-silica particles. They found that the size of nano-silica particles as well as silica loading affected the pore size and cell density. There are are also studies reported on enhancing the pore properties of polymer foams by modifying the surface of silica nanoparticles (Rende et al., 2013) and controlling cell size and number of cells by using surfactant (Eaves, 2004). It is found that surfactants can produce a higher miscibility rate of the polymer blends by reducing surface tension. On the other hand, cell openers can be utilized to improve the dimensional stability of the foam.
   Generally, polymer foam can be prepared either by thermoplastic or a thermoset polymer. A thermoplastic-based foam usually has characteristics of stable sphere dimension if foaming conditions like temperature are adequately controlled at a temperature near either Tg or Tm of the polymer. On the other hand, stable dimension thermoset-based foam only can be successfully prepared when the appropriate degree of curing or cross-linking for foaming and cell stabilization are satisfied. In case of thermoplastic elastomer (TPE) that has combinational properties of thermoplastic polymer and rubber is more likely complicated to be foamed as it may shrink and less uniform if the cross-linked chains are reduced, low solubility, as well as high blowing agent diffusivity and low rigidity, is possesses by the TPE (Sharudin & Ohshima, 2012).

The reliability of the numerical method of interpreting the thermal conductivity-cell properties relationships was supported by the analytical model of Maxwell-Eucken and further validated with the experimental results. Using the cell properties in terms of cell size, cell shape, and percentage of porosity, numerical results were able to clarify the thermal behavior of different SEBS cell shapes by their heat distribution profile. As shown in this study, the cell having an ellipse shape has lower thermal conductivity than the irregular one. However, the effect of cell size seems insignificant to the thermal conductivity value for each RVE study. The insignificant differences between the numerical and experimental results have shown it successfully demonstrated. Since preparing foam with different cell sizes while maintaining the percentage of porosity is challenging to control, the computerized approach would be affording a favorable thermal conductivity estimation alternative to enable the designing thermal insulators of elastomer-based foam at various cell properties.

    On behalf of all authors, the corresponding author states that they much appreciate Universiti Teknikal Malaysia Melaka (UTeM) supporting financially by Short term grant PJP/2020/FTKMP/PP/S01765, the Research Management Centre (RMC), Universiti Teknologi MARA (UiTM) for the financial support of the project under the grant 600-IRMI 5/3/LESTARI (042/2019) and Material Process Engineering Laboratory, Kyoto University for technical support during research completion.

Buryachenko V., 2007. Micromechanics of Heterogenous Materials. 1st Edition. USA: Springer, Dayton research institute, pp. 95–136

Carson J.K., Lovatt S.J., Tanner D.J., Cleland A.C., 2005. Thermal Conductivity Bounds for Isotropic Porous Materials. International Journal of Heat Mass Transfer, Volume 48(11), pp. 2150–2158

Chauvet M., Fages J., Sauceau M., Bailon F., 2016. Use of Starch as Nucleating Agent for the Extrusion Foaming of Poly-(Lactic Acid). In 15th European Meeting on Supercritical Fluids, EMSF 2016

Coste G., Negrell C., Caillol S., 2020. From Gas Release to Foam Synthesis, The Second Breath of Blowing Agents. European Polymer Journal, Volume 140(1). Doi: https://doi.org/10.1016/j.eurpolymj.2020.110029

Dai T.R., Chandrasekaran G., Chen J., Jackson C., Liu Y., Nian Q., Kwon B., 2021. Thermal Conductivity of Metal Coated Polymer Foam: Integrated Experimental and Modeling Study. International Journal of Thermal Science, Volume 169, No. 9. Doi: https://doi.org/10.1016/j.ijthermalsci.2021.107045

Eaves D., 2004. Handbook of Polymer Foams. Rapra Technology Limited, Shrewsbury, Shropshire, United Kingdom, pp. 72–73

Jana D.C., Sundararajan G., Chattopadhyay K., 2016. Effect of Porosity on Structure, Young's Modulus, and Thermal Conductivity of Sic Foams by Direct Foaming and Gel Casting. Journal American Ceramic Society, Volume 100(32), pp. 312–322

Lee W., Lee S., Izadi M., Kam S.I., 2016. Dimensionality-Dependent Foam Rhelogical Properties: How to Go from Linear to Radial Geometry for Foam Modelling and Simulation. SPE Annual Technical Conference and Exhibition, Houston, Society of Petroleum Engineers (SPE), Volume 21(5), pp. 1669–1687

Li X., Park W., Chen Y.P., Ruan X., 2017. Effect of Particle Size and Aggregation on Thermal Conductivity of Metal-Polymer Nanocomposites. Journal of Heat Transfer, Volume 139(2), pp. 022401-1–022401-5

Mantaranon N., Chirachanchai S. 2016. Polyoxymethylene Foam: From an Investigation of Key Factors Related to Porous Morphologies and Microstructure to the Optimization of Foam Properties. Polymer, Volume 96(8), pp. 54–62

Marshall A.L., 2012. Examination of the Interconnectivity of SiC in a Si:SiC Composite System. The American Ceramic Society, In: Ceramic Engineering and Science Proceedings, Volume 33(10), No. 17, pp. 193–199

Monie F., Vidil T., Grignard B., Cramail H., Detrembleur C., 2021. Self-foaming polymers: Opportunities for the Next Generation of Personal Protective Equipment. Materials Science and Engineering: R: Reports, Volume 145(12). Doi: https://doi.org/10.1016/j.mser.2021.100628

Moratal D., 2010. Finite Element Analysis. IntechOpen, London, UK, ISBN 978-953-307-123-7

Moumen A.E., Kanit T., Imad A., Minor H.E., 2015. Computational Thermal Conductivity in Porous Materials Using Homogenization Techniques: Numerical and Statistical Approaches. Computational Materials Science, Volume 97, pp. 148–158

Muayad A.S., Mohammed A.D., Hamad K.M., 2020. Kinetic Study of Air Bubbles-Cetyltrimethylammonium Bromide (CTAB) Surfactant for Recovering Microalgae Biomass in a Foam Flotation Column. International Journal of Technology, Volume 11(3), pp. 440–449

Rainglet B., Chalamet Y., Legar´e V.B., Delage K., Forest C., Cassagnau P., 2021. Polypropylene Foams Under CO2 Batch Conditions: From Formulation and Rheological Modeling to Cell-Growth Simulation. Polymer, Volume 218(12)

Rende, D., Schadler, L.S. and Ozisik, R., 2013. Controlling Foam Morphology of Poly (Methyl Methacrylate) Via Surface Chemistry and Concentration of Silica Nanoparticles and Supercritical Carbon Dioxide Process Parameters. Journal of Chemistry, Volume 2013

Roedel S., Souza J.C.M., Silva F.S., Guimarães J.M., Fredel M.C., Henriques B., 2018. Optimized Route for The Production of Zirconia Structures With Controlled Surface Porosity for Biomedical Application. Ceramic International, Volume 44(11), No. 74, pp. 22496–22503

Sharudin R.W., Ohshima M., 2012. Preparation of Microcellular Thermoplastic Elastomer Foams from Polystyrene-b-polybutadiene-b-polystyrene (SEBS) and their Blends with Polystyrene. Journal of Applied Polymer Science, Volume 128(4), pp. 2245–2254

Solbakken J.S., Aarra M.G., 2021. CO2 Mobility Control Improvement Using N2-Foam at High Pressure And High Temperature Conditions. International Journal of Greenhouse Gas Control, Volume 109(30), pp. 103392. https://doi.org/10.1016/j.ijggc.2021.103392

Sundarram S. S., Li W., 2013. On Thermal Conductivity of Micro-and Nanocellular Polymer Foams. Journal of Applied Polymer Science, Volume 53(9), No. 11, pp. 1901–1909

Zakyan S.E., Famili M.H.N., Ako M, 2014. Controlling Foam Morphology of PS via Surface Chemistry, Size and Concentration of Nanosilica Particles. Journal of Material Science, Volume 49(18), pp. 6225–6239

Zulkarnain M, Fadzil M.A., Rahida Wati Sharudin, 2017. Algorithm of Pores Distribution Model for Analysis And Measurement of Thermal Conductivity of Polypropylene Porous Material. International Journal of Technology, Volume 8(3), pp. 398–407