Elastomers and Composites

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Analytical Techniques for Measurement of Crosslink Densities of Rubber Vulcanizates

  • Received : 2019.07.11
  • Accepted : 2019.08.01
  • Published : 2019.09.30
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Abstract

It is important to analyze crosslink densities of rubber articles because the physical properties are dependent on the crosslink densities. In this paper, analytical techniques for the measurement of crosslink densities of rubber vulcanizates are described. The most widely used method to measure the crosslink density is a swelling method combined with the Flory-Rehner equation. Application of the interaction parameter (${\chi}$) of rubber and swelling solvent is critical because the crosslink density is absolutely dependent on the ${\chi}$ value. Methods for obtaining ${\chi}$ employ not only solubility parameters of the polymer and swelling solvent but also inverse gas chromatography (IGC). The solubilities of rubbers can be obtained using micro differential scanning calorimetry (${\mu}DSC$), intrinsic viscosity measurement, and UV-visible spectroscopy. Nuclear magnetic resonance (NMR) spectroscopy has been also used for the measurement of the crosslink density using the $T_2$ relaxation time, which is determined by spin-spin relaxation in solid-state NMR. For sulfur-cured rubber vulcanizates, crosslink densities according to the crosslink types of mono-, di-, and polysulfides are measured by treating the rubber samples with a chemical probe composed of thiol and amine compounds. Measurement methods of physical crosslinking by filler, crystallization, and ionic bonding have also been introduced.

Keywords

References

  1. A. S. Aprem, K. Joseph, and S. Thomas, "Recent developments in crosslinking of elastomers", Rubber Chem. Technol., 78, 458 (2005). https://doi.org/10.5254/1.3547892
  2. M. Akiba, "Vulcanization and crosslinking in elastomers", Prog. Polym. Sci., 22, 475 (1997). https://doi.org/10.1016/S0079-6700(96)00015-9
  3. F. Zhao, W. Bi, and S. Zhao, "Influence of crosslink density on mechanical properties of natural rubber vulcanizates", J. Macromol. Sci. B, 50, 1460 (2011). https://doi.org/10.1080/00222348.2010.507453
  4. M. Nasir and G. K. Teh, "The effects of various types of crosslinks on the physical properties of natural rubber", Eur. Polym. J., 24, 733 (1988). https://doi.org/10.1016/0014-3057(88)90007-9
  5. M. Tosaka, S. Murakami, S. Poompradub, and S. Kohjiya, "Orientation and crystallization of natural rubber network as revealed by WAXD using synchrotron radiation", Macromolecules, 37, 3299 (2004). https://doi.org/10.1021/ma0355608
  6. J. Lal, "Effect of crosslink structure on properties of natural rubber", Rubber Chem. Technol., 43, 664 (1970). https://doi.org/10.5254/1.3547280
  7. R. Fan, Y. Zhang, C. Huang, Y. Zhang, Y. Fan, and K. Sun, "Effect of crosslink structures on dynamic mechanical properties of natural rubber vulcanizates under different aging conditions", J. Appl. Polym. Sci., 710, 81 (2001).
  8. D. Balladares, S. Toki, T. Z. Sen, B. Yalcin, and M. Cakmak, "The effect of natural rubber crosslink density on real time birefringence, true stress and true strain behavior", Macromol. Symp., 185, 149 (2002). https://doi.org/10.1002/1521-3900(200208)185:1<149::AID-MASY149>3.0.CO;2-8
  9. C. M. Kok and V. H. Yee, "The effects of crosslink density and crosslink type on the tensile and tear strengths of NR, SBR and EPDM gum vulcanizates", Euro. Polym. J., 22, 341 (1986). https://doi.org/10.1016/0014-3057(86)90203-X
  10. Y. Minoura, S. Yamashita, H. Okamoto, T. Matsuo, M. Izawa, and S. Kohmoto, "Crosslinking and mechanical property of liquid rubber. II. Curative effect of aromatic diols", J. Appl. Polym. Sci., 22, 3101 (1978). https://doi.org/10.1002/app.1978.070221106
  11. R. Hagen, L. Salmen, and B. Stengerg, "Effects of the type of crosslink on viscoelastic properties of natural rubber", J. Polym. Sci. B., 34, 1997 (1996). https://doi.org/10.1002/(SICI)1099-0488(19960915)34:12<1997::AID-POLB5>3.0.CO;2-N
  12. S.-S. Choi and E. Kim, "A Novel system for measurement of types and densities of sulfur crosslinks of a filled rubber vulcanizate", Polym. Test., 42, 62 (2015). https://doi.org/10.1016/j.polymertesting.2014.12.007
  13. R. W. Layer, "A postcrosslinking accelerator system for natural rubber based on thiocarbamoyl sulfonamides", Rubber Chem. Technol., 60, 89 (1987). https://doi.org/10.5254/1.3536124
  14. W. Salgueiro, A. Marzocca, A. Somoza, G. Consolati, S. Cerveny, F. Quasso, and S. Goyanes, "Dependence of the network structure of cured styrene butadiene rubber on the sulphur content", Polymer, 45, 6037 (2004). https://doi.org/10.1016/j.polymer.2004.05.008
  15. J. I. Cunneen and R. M. Russell, "Occurrence and prevention of changes in the chemical structure of natural rubber tire tread vulcanizates during service", Rubber Chem. Technol., 43, 1215 (1970). https://doi.org/10.5254/1.3547319
  16. B. Saville and A. A. Watson, "Structural characterization of sulfur vulcanized rubber networks", Rubber Chem. Technol., 40, 100 (1967). https://doi.org/10.5254/1.3539039
  17. D. S. Campbell, "Structural characterization of vulcanizates part X. Thiol-disulfide interchange for cleaving disulfide crosslinks in natural rubber vulcanizates", J. Appl. Polym. Sci., 13, 1201 (1969). https://doi.org/10.1002/app.1969.070130609
  18. D. Kiroski, J. Sims, A. L. Gregory, and D. E. Packham, "The use of thiolamine chemical probes in network characterisation of NBR vulcanizates", Kautsch. Gummi Kunst, 50, 716 (1997).
  19. L. M. Lopez, A. B. Cosgrove, J. P. Hernandez-Ortiz, and T. A. Osswald, "Modeling the vulcanization reaction of silicon rubber", Polym. Eng. Sci., 47, 675 (2007). https://doi.org/10.1002/pen.20698
  20. A. M. Zaper and J. L. Koenig, "Solid state carbon-13 NMR studies of vulcanized elastomers. II, Sulfur vulcanization of natural rubber", Rubber Chem. Technol., 60, 252 (1987). https://doi.org/10.5254/1.3536129
  21. V. Ouehacek and A. Kuta, "A study of sulfur-free thiuram vulcanization using differential scanning calorimeter", J. Polym. Sci. A Polym. Chem., 27, 1089 (1989).
  22. S.-H. Chough and D.-H. Chang, "Kinetics of sulfur vulcanization of NR, BR, SBR, and their blends using a rheometer and DSC", J. Appl. Polym. Sci., 61, 449 (1996). https://doi.org/10.1002/(SICI)1097-4628(19960718)61:3<449::AID-APP7>3.0.CO;2-I
  23. A. J. Tinker, "Crosslink distribution and interfacial adhesion in vulcanized blends of NR and NBR", Rubber Chem. Thechnol., 63, 503 (1990). https://doi.org/10.5254/1.3538269
  24. W. Salgueiro, A. Somozaa, A. J. Marzocca, G. Consolati, and F. Quasso, "Evolution of the crosslink structure in the elastomers NR and SBR", Rad. Phys. Chem., 76, 142 (2007). https://doi.org/10.1016/j.radphyschem.2006.03.019
  25. L. D. Loan, "Peroxide crosslinking of ethylene-propylene rubber", J. Polym. Sci. A, 2, 3053 (1964).
  26. J. P. Berry and W. F. Watson, "Stress relaxation of peroxide and sulfur vulcanizates of natural rubber", J. Polym. Sci., 18, 201 (1955). https://doi.org/10.1002/pol.1955.120188804
  27. Y. Ikeda, Y. Yasuda, S. Makino, S. Yamamoto, M. Tosaka, K. Senoo, and S. Kohjiya, "Strain-induced crystallization of peroxide-crosslinked natural rubber", Polymer, 48, 1171 (2007). https://doi.org/10.1016/j.polymer.2007.01.006
  28. L. Gonzalez, A. Rodrigues, A. Marcos, and C. Chamorro, "Crosslink reaction mechanism of diene rubber with dicumyl peroxide", Rubber Chem. Technol., 69, 203 (1996). https://doi.org/10.5254/1.3538365
  29. Q. Yu and S. Zhu, "Peroxide crosslinking of isotactic and syndiotactic polypropylene", Polymer, 40, 2961 (1999). https://doi.org/10.1016/S0032-3861(98)00519-9
  30. E. Borsig, A. Fiedlerova, L. Rychla, M. Lazer, M. Ratzsch, and G. Haudel, "Crosslinking of polypropylene-polyethylene blends by peroxide and the effect of pentaerythritol tetrallyl ether", J. Appl. Polym. Sci., 37, 467 (1989). https://doi.org/10.1002/app.1989.070370213
  31. R. P. Lattimer, R. A. Kinsey, R. W. Layer, and C. K. Rhee, "The mechanism of phenolic resin vulcanization of unsaturated elastomers", Rubber Chem. Technol., 62, 107 (1989). https://doi.org/10.5254/1.3536228
  32. V. Tanrattanakul, K. Kosonmetee, and P. Laokicharoen, "Polypropylene/natural rubber thermoplastic elastomer: Effect of phenolic resin as a vulcanizing agent on mechanical properties and morphology", J. Appl. Polym. Sci., 112, 3267 (2009). https://doi.org/10.1002/app.29816
  33. M. Duin and A. Souphanthong, "The chemistry of phenolformaldehyde resin vulcanization of EPDM: Part I. Evidence for methylene crosslinks", Rubber Chem. Technol., 68, 717 (1995). https://doi.org/10.5254/1.3538768
  34. A. Masa, S. Limori, R. Saito, T. Sakai, A. Kaesaman, and N. Lopattananon, "Strain-induced crystallization behavior of phenolic resin crosslinked natural rubber/clay nanocomposites", J. Appl. Polym. Sci., 132, 42580 (2015).
  35. W. Pechurai, K. Sahakaro, and C. Nakason, "Influence of phenolic curative on crosslink density and other related properties of dynamically cured NR/HDPE blends", J. Appl. Polym. Sci., 113, 1232 (2009). https://doi.org/10.1002/app.30036
  36. S.-S. Choi and O.-B. Kim, "Mass spectrometric monitoring of change of resole structures by compounding and curing of EPDM compound", Polym. Test., 58, 181 (2017). https://doi.org/10.1016/j.polymertesting.2016.12.032
  37. Z. Y. Ding, J. J. Aklonis, and R. Salovey, "Model filled polymers. VI. Determination of the crosslink density of polymeric beads by swelling", J. Polym. Sci. B Polym. Phys., 29, 1035 (1991). https://doi.org/10.1002/polb.1991.090290815
  38. O. Kraus, "Swelling of filler-reinforced vulcanizates", J. Appl. Polym. Sci., 7, 861 (1963). https://doi.org/10.1002/app.1963.070070306
  39. H. Kato and H. Fujita, "Development of synergistic curing systems for polychloroprene", Rubber Chem. Technol., 55, 949 (1982). https://doi.org/10.5254/1.3535924
  40. H. Inomata, N. Wada, Y. Yagi, S. Goto, and S. Saito, "Swelling behaviours of N-alkylacrylamide gels in water: effects of copolymerization and crosslinking density", Polymer, 36, 875 (1995). https://doi.org/10.1016/0032-3861(95)93120-B
  41. K. Y. Lee, J. A. Rowley, P. Eiselt, E. M. Moy, K. H. Bouhadir, and D. J. Mooney, "Controlling mechanical and swelling properties of alginate hydrogels independently by cross-linker type and cross-linking density", Macromolecules, 33, 4291 (2000). https://doi.org/10.1021/ma9921347
  42. G. M. Eichnbaum, P. F. Kiser, A. V. Dobrynin, S. A. Simon, and D. Needham, "Investigation of the swelling response and loading of ionic microgels with drugs and proteins: the dependence on cross-link density", Macromolecules, 32, 4867 (1999). https://doi.org/10.1021/ma981945s
  43. N. A. Peppas and E. W. Merrill, "Crosslinked poly(vinyl alcohol hydrogels as swollen elastic networks", J. Appl. Polym. Sci., 21, 1763 (1977). https://doi.org/10.1002/app.1977.070210704
  44. M. Amin, G. M. Nasr, G. Attia, and A. S. Gomaa, "Determination of the crosslink density of conductive ternary rubber vulcanizates by solvent penetration", Mater. Lett., 28, 207 (1996). https://doi.org/10.1016/0167-577X(96)00063-8
  45. B. Guo, F. Chen, Y. Lei, X. Liu, J. Wang, and D. Jia, "Styrenebutadiene rubber/halloysite nanotubes nanocomposites modified by sorbic acid", Appl. Surf. Sci., 255, 7329 (2009). https://doi.org/10.1016/j.apsusc.2009.03.092
  46. 정유연, "에틸렌-비닐 아세테이트 공중합체의 상호작용 상수와 용해도 상수에 대한 고찰", 세종대학교 대학원 석사학위논문, 2018.
  47. J. K. Kim and M. A. Paglicawan, "Effect of devulcanizer on the properties of natural rubber vulcanizates", Philippine J. Sci., 133, 87 (2004).
  48. Z. Hrnjak-Murgic, J. Jelencic, M. Bravar, and M. Marovic, "Influence of the network on the interaction parameter in system EPDM vulcanizate-solvent", J. Appl. Polym. Sci., 65, 991 (1997). https://doi.org/10.1002/(SICI)1097-4628(19970801)65:5<991::AID-APP17>3.0.CO;2-V
  49. W. Salgueiro, A. Somoza, I. L. Torriani, and A. J. Marzocca, "Cure temperature influence on natural rubber-a small angle X-ray scattering study", J. Polym. Sci. B Polym. Phys., 45, 2966 (2007). https://doi.org/10.1002/polb.21293
  50. R. W. Brotzman and P. J. Flory, "Elastic behavior of cis-1,4-polybutadiene", Macromolecules, 20, 351 (1987). https://doi.org/10.1021/ma00168a021
  51. R. M. Masegosa, M. G. Prolongo, and A. Horta, "g interaction parameter of polymer - solvent systems", Macromolecules, 19, 1478 (1986). https://doi.org/10.1021/ma00159a033
  52. S. Seghar, N. Ait Hocine, V. Mittal, S. Azem, A. F. Al-Zohbi, B. Schmaltz, and N. Poirot, "Devulcanization of styrene butadiene rubber by microwave energy: Effect of the presence of ionic liquid", eXPRESS Polym. Lett., 9, 1076 (2015). https://doi.org/10.3144/expresspolymlett.2015.97
  53. J. Kruzelak, R. Dosoudil, and I. Hudec, "Thermooxidative aging of rubber composites based on NR and NBR with incorporated strontium ferrite", J. Elast. Plast., 50, 71 (2017). https://doi.org/10.1177/0095244317699986
  54. J. Kruzelak, M. Matvejova, R. Dosoudil, and I. Hudec, "Barium and strontium ferrite-filled composites based on NBR and SBR", J. Elast. Plast., 51, 421 (2019). https://doi.org/10.1177/0095244318792036
  55. W. L. Hergenrother, "Characterization of networks from the peroxide cure of polybutadiene", J. Appl. Polym. Sci., 16, 2611 (1972). https://doi.org/10.1002/app.1972.070161014
  56. W. O. Parker, A. Ferrando, D. Ferri, and V. Canepari, "Crosslink density of a dispersed rubber measured by $^{129}Xe$ chemical shift", Macromolecules, 40, 5787 (2007). https://doi.org/10.1021/ma070793a
  57. F. Guom, J. W. Andreasen, M. E. Vigild, and S. Ndoni, "Influence of 1,2-PB matrix cross-linking on structure and properties of selectively etched 1,2-PB- b-PDMS block copolymers", Macromolecules, 40, 3669 (2007). https://doi.org/10.1021/ma062947c
  58. N. Z. Noriman, H. Ismail, and A. A. Rashid, "Characterization of styrene butadiene rubber/recycled acrylonitrile-butadiene rubber (SBR/NBRr) blends: The effects of epoxidized natural rubber (ENR-50) as a compatibilizer", Polym. Test., 29, 200 (2010). https://doi.org/10.1016/j.polymertesting.2009.11.002
  59. M. I. Avadanei, "Photocrosslinking of 1,2-polybutadiene and characteristics of the crosslinked system", J. Macromol. Sci. B, 51, 313 (2011). https://doi.org/10.1080/00222348.2011.596788
  60. S. Saeki, J. C. Holste, and D. C. Bonner, "Vapor-liquid equilibria for polybutadiene and polyisoprene solutions", J. Polym. Sci. Polym. Phys., 20, 793 (1982). https://doi.org/10.1002/pol.1982.180200502
  61. R. S. Jessup, "Thermodynamic properties of the systems polybutadiene - benzene and polyisobutene - benzene", J. Res. Natl. Bur. Stand., 60, 47 (1958). https://doi.org/10.6028/jres.060.006
  62. E. C. Gregg and S. E. Katrenick, "Chemical structure in cis-1,4-polybutadiene vulcanizates. Model compound approach", Rubber Chem. Technol., 43, 549 (1970). https://doi.org/10.5254/1.3547273
  63. H. Nabil, H. Ismail, and A. R. Azura, "Effects of virgin ethylene-propylene-diene-monomer and its preheating time on the properties of natural rubber/recycled ethylene-propylene-diene-monomer blends", Mater. Design, 50, 27 (2013). https://doi.org/10.1016/j.matdes.2013.02.086
  64. J. Diez, R. M. Bellas, J. Lopez, and G. Santoro, "Study of the crosslink density, dynamo-mechanical behaviour and microstructure of hot and cold SBR vulcanizates", J. Polym. Res., 17, 99 (2010). https://doi.org/10.1007/s10965-009-9295-6
  65. S. Rolere, C. Bottier, L. Vaysse, J. Sainte-ABeuve, and F. Bonfils, "Characterisation of macrogel composition from industrial natural rubber samples: Influence of proteins on the macrogel crosslink density", eXPRESS Polym. Lett., 10, 408 (2016). https://doi.org/10.3144/expresspolymlett.2016.38
  66. J. H. Hildebrand and R. L. Scott, "The solubility of nonelectrolytes", Rheinhold Publishing Corporation, New York, 1950.
  67. C. M. Hansen, "The universality of the solubility parameter", Ind. Eng. Chem Pro. Res. Develop, 8, 2 (1969). https://doi.org/10.1021/i360029a002
  68. E. Stefanis and C. Panayiotou, "Prediction of Hansen solubility parameters with a new group-contribution method", Int. J. Thermophys, 29, 568 (2008). https://doi.org/10.1007/s10765-008-0415-z
  69. F. Gharagheizi, A. Eslamimanesh, A. H. Mohammadi, and D. Richon, "Group contribution-based method for determination of solubility parameter of nonelectrolyte organic compounds", Ind. Eng. Chem. Res., 50, 10344 (2011). https://doi.org/10.1021/ie201002e
  70. A. F. M. Barton, "Solubility parameters", Chem. Rev., 75, 731 (1975). https://doi.org/10.1021/cr60298a003
  71. K. Ito and J. E. Guillet, "Estimation of Solubility Parameters for Some Olefin polymers and copolymers by inverse gas chromatography", Macromolecules, 1163, 12 (1979).
  72. G. J. Price and I. M. Shillcock, "Inverse gas chromatographic measurement of solubility parameters in liquid crystalline systems", J. Chrom. A, 964, 199 (2002). https://doi.org/10.1016/S0021-9673(02)00651-9
  73. S. P. Carvalho, E. F. Lucas, G. Gonzalez, and L. S. Spinelli, "Determining Hildebrand solubility parameter by ultraviolet spectrscopy and microcalorimetry", J. Braz. Chem. Soc., 24, 1998 (2013).
  74. G. DiPaola-Baranyi and J. E. Guilletm, "Estimation of solubility parameters for poly(vinyl acetate) by inverse gas chromatography", J. Chrom. A, 166, 349 (1978). https://doi.org/10.1016/S0021-9673(00)95616-4
  75. 박희용, 이유라, 조혜성. 가황 고무 내 황 가교 결합 길이의 분석 방법. 특허출원 제10-2017-0124354, 2017.
  76. V. M. Litvinov, W. Barendswaard, and M. van Duin, "The density of chemical crosslinks and chain entanglements in unfilled EPDM vulcanizates as studied with low resolution, solid state $^{1}H$ NMR", Rubber Chem. Technol., 71, 105 (1998). https://doi.org/10.5254/1.3538466
  77. T. Saleesung, D. Reichert, K. Saalwachter, and C. Sirisinha, "Correlation of crosslink densities using solid state NMR and conventional techniques in peroxide-crosslinked EPDM rubber", Polymer, 56, 309 (2015). https://doi.org/10.1016/j.polymer.2014.10.057
  78. W. Gronski, U. Hoffmann, G. Simon, A. Wutzler, and E. Staraube, "Structure and density of crosslink in natural-rubber vulcanizates. A combined analysis by NMR spectroscopy, mechanical mearuement, and rubber-elastic theory", Rubber Chem. Technol., 65, 63 (1992). https://doi.org/10.5254/1.3538608
  79. G. Simon, K. Baumann, and W. Gronski, "Mc determination and molecular dynamics in crosslinked 1,4-cis-polybutadiene: a comparison of transversal proton and deuterium NMR relaxation", Macromolecules, 25, 3624 (1992). https://doi.org/10.1021/ma00040a003
  80. M. D. Ellul, A. H. Tsou, and W. Hu, "Crosslink densities and phase morphologies in thermoplastic vulcanizates", Polymer, 45, 3351 (2004). https://doi.org/10.1016/j.polymer.2004.03.029
  81. M. Garbarczyk, F. Grinberg, N. Nestle, and W. Kuhn, "A novel approach to the determination of the crosslink density in rubber materials with the dipolar correlation effect in low magnetic fields", J. Polym. Sci. B, Polym. Phys., 39, 2207 (2001). https://doi.org/10.1002/polb.1194
  82. W. Kuhn, P. Barth, P. Denner, and R. Muller, "Characterization of elastomeric materials by NMR-microscopy", Solid State Nucl. Magn. Reson., 6, 295 (1996). https://doi.org/10.1016/0926-2040(96)01236-2
  83. Y. K. Chae, W. Y. Kang, J.-H. Jang, and S.-S. Choi, "A simple NMR method to measure crosslink density of natural rubber composite", Polym. Test., 29, 953 (2010). https://doi.org/10.1016/j.polymertesting.2010.08.003
  84. M. K. Dibbanti, "Study of polymer crosslink density by time domain NMR spectroscopy", University of Milano-Bicocca, 2015.
  85. R. W. Layer, "A postcrosslinking accelerator system for natural rubber based on thiocarbamyl sulfonamides", Rubber Chem. Technol., 60, 89 (1987). https://doi.org/10.5254/1.3536124
  86. W. Salgueiro, A. Marzocca, A. Somoza, G. Consolati, S. Cerveny, F. Quasso, and S. Goyanes, "Dependence of the network structure of cured styrene butadiene rubber on the sulphur content", Polymer, 45, 6037 (2004). https://doi.org/10.1016/j.polymer.2004.05.008
  87. S.-S. Choi, I.-S. Kim, and C.-S. Woo, "Influence of TESPT content on crosslink types and rheological behaviors of natural rubber compounds reinforced with silica", J. Appl. Polym. Sci., 106, 2753 (2007). https://doi.org/10.1002/app.25744
  88. J. I. Cunneen and R. M. Russell, "Occurrence and prevention of changes in the chemical structure of natural rubber tire tread vulcanizates suring service", Rubber Chem. Technol., 43, 1215 (1970). https://doi.org/10.5254/1.3547319
  89. B. Saville and A. A. Watson, "Structural characterization of sulfur-vulcanized rubber networks", Rubber Chem. Technol., 40, 100 (1967). https://doi.org/10.5254/1.3539039
  90. D. S. Campbell, "Structural characterization of vulcanizates part X. Thiol-disulfide interchange for cleaving disulfide crosslinks in natural rubber vulcanizates", J. Appl. Polym. Sci., 13, 1201 (1969). https://doi.org/10.1002/app.1969.070130609
  91. D. Kiroski, J. Sims, A. L. Gregory, and D. E. Packham, "The use of thiol-amine chemical probes in network characterisation of NBR vulcanizates", Kautsch. Gummi Kunst., 50, 716 (1997).
  92. S.-S. Choi and E. Kim, "A novel system for measurement of types and densities of sulfur crosslinks of a filled rubber vulcanizate", Polym. Test., 42, 62 (2015). https://doi.org/10.1016/j.polymertesting.2014.12.007
  93. Z. Fei, C. Long, P. Qingyan, and Z. Shugao, "Influence of carbon black on crosslinking density of natural rubber", J. Macromol. Sci. B, 51, 1208 (2012). https://doi.org/10.1080/00222348.2012.664494
  94. J. Maitra and V. K. Shukla, "Cross-linking in hydrogels - A review", Am. J. Polym. Sci., 4, 25 (2014).
  95. G. Kraus, "Swelling of filler reinforced vulcanizates", J. Appl. Polym. Sci., 7, 3 (1963). https://doi.org/10.1002/app.1963.070070231
  96. K. Hwang, W. Kim, B. Ahn, H. Mun, E. Yu, D. Kim, G. Ryu, and W. Kim, "Effect of surfactant of the physical properties andcrosslink density of silica filled ESBR compounds and carbon black filled compounds", Elast. Compos., 53, 39 (2018). https://doi.org/10.7473/EC.2018.53.2.39