Soundproofing performance of flexible polyurethane foams as a fractal object

  • Sahar Abdollahi Baghban
  • Manouchehr KhorasaniEmail author
  • Gity Mir Mohamad Sadeghi


Noise pollution is one of the most severe environmental concerns due to its damaging effects on human health. This study aimed to evaluate the relationship between the acoustic damping behavior and fractal dimension (Df) of flexible polyurethane foams (FPUFs) manufactured by different synthesized linear saturated aliphatic polyesters (LSAP) resins, methylene diphenyl diisocyanate (MDI), etc. (isocyanate index = 110 & water content = 5%). Cellular and soundproofing properties of FPUFs were evaluated by an optical microscope and impedance tube device. Df was calculated by the box-counting method after binarization and image processing of FPUF images. Results indicate that by increasing Df from 1.5415 to 1.8554, the total sound absorption performance (S) of FPUFs improves by 43.07% and the maximum sound absorption coefficient reaches 0.98. The relation between S and Df was obtained as follows: Log(S) = 0.4583 Df + 2.6659, r2 = 0.9298. Generally, decreasing the cell size and increasing the cell size distribution and open-cell content, increase Df and irregularity of FPUFs. The results reveal that FPUFs with an optimum condition of cell size of 180–200 μm, open-cell content of 30%, and density of 110 (Kg.m−3) have the highest Df and can be a promising candidate as sound insulating materials.


Fractal dimension Soundproofing Flexible polyurethane foam Linear saturated aliphatic polyester resins Box-counting method 



The authors would like to acknowledge the Color & Polymer Research Center (CPRC) for the financial and their kind support.

Author contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Sahar Abdollahi Baghban. Also, the draft of the manuscript was written by Sahar Abdollahi Baghban under the supervision of Manouchehr Khorasani and Giti Mir Mohammad Sadeghi.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Gwon JG, Kim SK, Kim JH (2016) Sound absorption behavior of flexible polyurethane foams with distinct cellular structures. Mater Des 89:448–454CrossRefGoogle Scholar
  2. 2.
    Sung G, Kim JS, Kim JH (2017) Sound absorption behavior of flexible polyurethane foams including high molecular-weight copolymer polyol. Polym Adv Technol 29:852–859CrossRefGoogle Scholar
  3. 3.
    Tiuc AE, Vermeşan H, Gabor T, Vasile O (2016) Improved sound absorption properties of polyurethane foam mixed with textile waste. Energy Procedia 85:559–565CrossRefGoogle Scholar
  4. 4.
    Sung G, Kim JH (2017) Effect of high molecular weight isocyanate contents on manufacturing polyurethane foams for improved sound absorption coefficient. Korean J Chem Eng 34:1222–1228CrossRefGoogle Scholar
  5. 5.
    Shafigullin LN, Yurasov SY, Shayakhmetova GR, Shafigullina AN, Zharin ED (2017) Sound-absorbing polyurethane foam for the auto industry. Russ Eng Res 37:372–374CrossRefGoogle Scholar
  6. 6.
    Park JH, Minn KS, Lee HR, Yang SH, Yu CB, Pak SY, Oh CS, Song YS, Kang YJ, Youn JR (2017) Cell openness manipulation of low-density polyurethane foam for efficient sound absorption. J Sound Vib 406:224–236CrossRefGoogle Scholar
  7. 7.
    Sung G, Kim SK, Kim JW, Kim JH (2016) Effect of isocyanate molecular structures in fabricating flexible polyurethane foams on sound absorption behavior. Polym Test 53:156–164CrossRefGoogle Scholar
  8. 8.
    Gwon JG, Kim SK, Kim JH (2016) Development of cell morphologies in manufacturing flexible polyurethane urea foams as sound absorption materials. J Porous Mater 23:465–473CrossRefGoogle Scholar
  9. 9.
    Cinelli P, Anguillesi I, Lazzeri (2013) A green synthesis of flexible polyurethane foams from liquefied lignin. Eur Polym J 49:1174–1184CrossRefGoogle Scholar
  10. 10.
    Lan Z, Daga AR, White House R, McCarthy S, Schmidt D (2014) Structure–properties relations in flexible polyurethane foams containing a novel bio-based crosslinker. Polym 55:2635–2644CrossRefGoogle Scholar
  11. 11.
    Simón D, Ade L, Rodríguez JF, Borreguero AM (2016) Glycolysis of high resilience flexible polyurethane foams containing polyurethane dispersion polyol. Polym Degrad Stab 133:119–130CrossRefGoogle Scholar
  12. 12.
    Oliviero M, Verdolotti L, Stanzione M, Lavorgna M, Iannace S, Tarello M, Sorrentino A (2017) Bio-based flexible polyurethane foams derived from succinic polyol: mechanical and acoustic performances. Appl Polym Sci 134:45113CrossRefGoogle Scholar
  13. 13.
    Arenas JP, Ugarte F (2016) A note on a circular panel sound absorber with an elastic boundary condition. Appl Ac 114:10–17CrossRefGoogle Scholar
  14. 14.
    Mahmoud AA, Ader Nasr EA, Hamed Maamoun AA (2017) The influence of polyurethane foam on the insulation characteristics of mortar pastes. J Miner Mater Charact Eng 5:49–61Google Scholar
  15. 15.
    Chuang YC, Li TT, Huang CH, Huang CL, Lou CW, Chen YS, Lin JH (2016) Protective rigid fiber-reinforced polyurethane foam composite boards: sound absorption, drop-weight impact and mechanical properties. Fiber Polym 17:2116–2123CrossRefGoogle Scholar
  16. 16.
    Abdessalam H, Abbès B, Abbès F, Li Y, Guo YQ (2017) Prediction of acoustic properties of polyurethane foams from the macroscopic numerical simulation of foaming process. Appl Ac 120:129–136CrossRefGoogle Scholar
  17. 17.
    Gama N, Silva R, Carvalho APO, Ferreirad A, Barros-Timmons A (2017) Sound absorption properties of polyurethane foams derived from crude glycerol and liquefied coffee grounds. Polyol Polym Test 62:13–22CrossRefGoogle Scholar
  18. 18.
    Zhang X, Shen Q, Zhang X, Pan H, Lu Y (2016) Graphene oxide-filled multilayer coating to improve flame-retardant and smoke suppression properties of flexible polyurethane foam. J Mater Sci 51:10361–10374CrossRefGoogle Scholar
  19. 19.
    Sung G, Kim JH (2017) Influence of filler surface characteristics on morphological, physical, acoustic properties of polyurethane composite foams filled with inorganic fillers. Compos Sci Technol 146:147–154CrossRefGoogle Scholar
  20. 20.
    Liu Y, He J, Yang R (2017) The synthesis of melamine-based polyether polyol and its effects on the flame retardancy and physical–mechanical property of rigid polyurethane foam. J Mater Sci 52:4700–4712CrossRefGoogle Scholar
  21. 21.
    Verdejo R, Stämpfli R, Alvarez-Lainez M, Mourad S, Rodriguez-Perez MA, Brühwiler PA, Shaffer M (2009) Enhanced acoustic damping in flexible polyurethane foams filled with carbon nanotubes. Compos Sci Technol 69:1564–1569CrossRefGoogle Scholar
  22. 22.
    Yang XH, Ren SW, Wang WB, Liu X, Xin FX, Lu TJ (2015) A simplistic unit cell model for sound absorption of cellular foams with fully/semi-open-cells. Compos Sci Technol 118:276–283CrossRefGoogle Scholar
  23. 23.
    Bahrambeygi H, Sabetzadeh N, Rabbi A, Nasouri K, Mousavi Shoushtari A, Babaei MR (2013) Nanofibers (PU and PAN) and nanoparticles (Nanoclay and MWNTs) simultaneous effects on polyurethane foam sound absorption. J Polym Res 20:72. CrossRefGoogle Scholar
  24. 24.
    Sung G, Kim JW, Kim JH (2016) Fabrication of polyurethane composite foams with magnesium hydroxide filler for improved sound absorption. J Ind Eng Chem 44:99–104CrossRefGoogle Scholar
  25. 25.
    Garrett JT, Xu R, Cho J, Runt J (2003) Phase separation of diamine chain-extended poly (urethane) copolymers: FT-IR spectroscopy and phase transitions. Polym 44:2711–2719CrossRefGoogle Scholar
  26. 26.
    Ning L, De-Ning W, Sheng-Kang Y (1996) Crystallinity and hydrogen bonding of hard segments in segmented poly (urethane-urea) copolymers. Polym 37:3577–3583CrossRefGoogle Scholar
  27. 27.
    Heintz AM, Duffy DJ, Nelson CM, Hua Y, Hsu SL, Suen W, Paul CW (2005) A spectroscopic analysis of the phase evolution in polyurethane foams. Macromol 38:9192–9199CrossRefGoogle Scholar
  28. 28.
    Ning L, De-Ning W, Sheng-Kang Y (1997) Hydrogen-bonding properties of segmented polyether poly (urethane-urea) copolymer. Macromol 30:4405–4409CrossRefGoogle Scholar
  29. 29.
    Ugarte L, Saralegi A, Fernandez R, Martín L, Corcuera M, Eceiza A (2014) Flexible polyurethane foams based on 100% renewably sourced polyols. Ind Crop Prod 62:545–551CrossRefGoogle Scholar
  30. 30.
    Xia H, Song M, Zhang Z, Richardson M (2007) Microphase separation, stress relaxation, and creep behavior of polyurethane nanocomposites. J Appl Polym Sci 103:2992–3002CrossRefGoogle Scholar
  31. 31.
    Yilgor I, Yilgor E, Wilkes GL (2015) Critical parameters in designing segmented polyurethanes and their effect on morphology and properties: a comprehensive review. Polym 58:A1–A36CrossRefGoogle Scholar
  32. 32.
    Aneja A, Wilkes GL, Yilgor I, Yilgor E, Yurtsever E (2003) Exploring urea phase connectivity in molded flexible polyurethane foam formulations using LiBr as a probe. J Macromol Sci Phys 42:125–1139CrossRefGoogle Scholar
  33. 33.
    Kaushiva B, McCartney S, Rossmy G, Wilkes G (2000) Surfactant level influences on structure and properties of flexible slabstock polyurethane foams. Polym 41:285–310CrossRefGoogle Scholar
  34. 34.
    Rightor E, Urquhart S, Hitchcock A, Ade H, Smith A, Mitchell G, Priester R, Aneja A, Appel G, Wilkes G (2002) Identification and quantitation of urea precipitates in flexible polyurethane foam formulations by X-ray spectromicroscopy. Macromol 35:5873–5882CrossRefGoogle Scholar
  35. 35.
    Onck PR, Andrews EW, Gibson LJ (2001) Size effects in ductile cellular solids. Part I: modeling. Int J Mech Sci 43:681–699CrossRefGoogle Scholar
  36. 36.
    Javni I, Song K, Lin J, Petrovic ZS (2011) Structure and properties of flexible polyurethane foams with nano-and micro-fillers. J Cell Plast 47:357–372CrossRefGoogle Scholar
  37. 37.
    Gayathri R, Vasanthakumari R, Padmanabhan C (2013) Sound absorption, thermal and mechanical behavior of polyurethane foam modified with nano silica, nano-clay and crumb rubber fillers. Int J Sci Eng Res 4:301–308Google Scholar
  38. 38.
    Kaushiva B, Wilkes G (2000) Alteration of polyurea hard domain morphology by diethanolamine (DEOA) in molded flexible polyurethane foams. Polym 41:6981–6986CrossRefGoogle Scholar
  39. 39.
    Mosanenzadeh SG, Naguib HE, Park CB, Atalla N (2014) Development of polylactide open-cell foams with bimodal structure for high-acoustic absorption. J Appl Polym Sci 131:39518CrossRefGoogle Scholar
  40. 40.
    Mingheng SH, Xiaochuan L, Yongping CH (2006) Determination of effective thermal conductivity for polyurethane foam by use of fractal method. SCI, CHINA SER E 49(4):468–475CrossRefGoogle Scholar
  41. 41.
    Ru J, Kong B, Ya L, Wang X, Fan T, Zhang D (2015) Microstructure and sound absorption of porous copper prepared by resin curing and foaming method. Mater Lett 139:318–321CrossRefGoogle Scholar
  42. 42.
    Wang F, Li Z, Chen H, Lv Q, Silagi W, Chen Z (2017) Fractal characterization of dynamic structure of foam transport in porous media. J Molecular Liq 241:675–683CrossRefGoogle Scholar
  43. 43.
    RuiDong P, YanCong Y, Yang J, LingTao M, YongMing Y (2011) Computation of fractal dimension of rock pores based on gray CT images. Chin Sci Bull 56(31):3346–3357CrossRefGoogle Scholar
  44. 44.
    Perez L, Lascano S, Aguilar C, Domancic D, Alfonso I (2015) Simplified fractal FEA model for the estimation of the Young’s modulus of Ti foams obtained by powder metallurgy. Mater Des 83:276–283CrossRefGoogle Scholar
  45. 45.
    Abdollahi Baghban S, Khorasani M, Mir Mohamad Sadeghi G (2018) Soundproofing flexible polyurethane foams: the impact of polyester chemical structure on the microphase separation and acoustic damping. J Appl Polym Sci 135:46744CrossRefGoogle Scholar
  46. 46.
    Abdollahi Baghban S, Khorasani M, Mir Mohamad Sadeghi G (2018) Acoustic damping flexible polyurethane foams: effect of isocyanate index and water content on the soundproofing. J Appl Polym Sci 136:47363CrossRefGoogle Scholar
  47. 47.
    Abdollahi Baghban S, Khorasani M, Mir Mohamad Sadeghi G (2019) Soundproofing flexible polyurethane foams: effect of chemical structure of chain extenders on micro-phase separation and acoustic damping. J Cell Plast 1:1–19. CrossRefGoogle Scholar

Copyright information

© The Polymer Society, Taipei 2020

Authors and Affiliations

  1. 1.Polymer Engineering, and Color Technology DepartmentAmirkabir University of TechnologyTehranIran

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