A determination of crosslink density from compression modulus data

Melley, R. E.; Stuckey, J. E.

doi:10.1002/app.1970.070140912

Cited by 11 publications

(6 citation statements)

References 6 publications

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“…Results reported by other observers [ 13 , 15 – 20 , 32 – 34 , 36 , 48 , 56 – 65 ] agree with the present work in showing that the modulus increases linearly with crosslinking for the higher degrees of cross-linking. The line likewise almost invariably has a slope greater than that predicted from the cross-linking.…”

Section: Possible Refinements Of Simple Theorysupporting

confidence: 93%

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Modulus of natural rubber cross-linked by dicumyl peroxide. III. Some molecular interpretations, possible refinements of theory, and conclusions

Wood¹

1976

J. RES. NATL. BUR. STAN. SECT. A.

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Th e s hea r modulu s G = 5.925 X 10 -3(Jp -0.45) T + G* Wa rt I), it s e ne rgy co mpon e nt G * = 0.0684 (jjJ -0.45) +2.70 W a rt 11 ), and th e numbe r of e ffec ti ve s ub-c ha in s pe r unit volum e Ve= (G -G* )IRT a re giv e n de tail ed mo lec ul a r consid e ra tio n. G is give n in Mdyn c m -2 for rubbe r cross-link ed by addin g p parts of di c umyl pe roxid e pe r hundre d of rubbe r, and heatin g until a fr ac ti on f of th e pero xid e is dec o mpose d. v" is fo und to be a pproximate ly twi ce th e de ns it y of c ross-link s, afte r a co rrecti o n for impuriti es a nd c ha in end s is mad e . It ca n not be co mputed as GI RT, s in ce on ly th e e ntropy co mpo ne nt of 1110dulu s is re lat e d to li e . Th e s ub-c ha in s fo r th e most hi ghl y cross -link ed rubber s s tudi ed had a m olec ul a r weight of abou t 575 g 11101 -' , corres po ndin g to abo ut 8 iso pre ne unit s . The modulus corres pondin g to no add ed c ross-link s is not ze ro. It is d ete rmin ed c hi e fiy by th e e ner gy compo ne nt of th e modulu s; it d oes not arise from entan gle me nts. Th e " front fa c tor" is found to be unity.An e xt e ns ive literature s urve y yie ld s valu es of the q uant it y RN (v,), whe re \jI (V2) is th e FloryRe llll e r e quation fun c tion of v" th e e quilibrium volume fra cti on ob tain ed by s we llin g th e c ross -linke d rubbe r. RT\jI (v,) is found to be grea te r th an G -G*, but not as large a s G it se lf. Ke y word s: C ross-li nk in g of rubb e r; di c um yl pe roxide ; e lasti c it y th eo ry of rub ber: e nta ngle me nt s in rubbe r; gel point ; molec ular int er pretation of rubbe r e las ti c ity ; modulu s of rubbe r ; rubbe r elas ti c it y; s tati sti c al th eor y of rubbe r elas ti c ity; s we llin g of rubbe r ne t wo rk. . IntroductionThe fir st paper in thi s series Part I [1] I presented experimen tal data on th e c han ge of modulus with temperature and cross -linkin g for natural rubbe r cross-linked by dicumyl peroxide ,The results we re presented in th e form of the following equation: The present paper makes much more de tailed molecular interpretations of the results than the second paper and e xamines the conseque nces of several refin e ments which might be mad e in the application of the theory, G=S (jp + B)T + H(fp +B

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Section: Possible Refinements Of Simple Theorysupporting

confidence: 93%

“…The purity of the pale crepe rubber may be estimated as normally about 93 percent. The purity of the “recrystallized” dicumyl peroxide was not measured here, but values near 95 percent have been reported [ 14 , 31 , 37 , 45 – 48 ].…”

Section: Possible Refinements Of Simple Theorymentioning

confidence: 99%

Modulus of natural rubber cross-linked by dicumyl peroxide. III. Some molecular interpretations, possible refinements of theory, and conclusions

Wood¹

1976

J. RES. NATL. BUR. STAN. SECT. A.

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“…9 However, the most common techniques to determine the cross-link density are mechanical measurements, [10][11][12][13][14][15] NMR spectroscopy, [16][17][18][19][20][21][22][23] and equilibrium swelling. [24][25][26][27][28] Although some of the previously mentioned techniques give some extra information about the structure of the network, the equilibrium swelling experiment is nowadays the most widely used approach in rubber science and technology.…”

Section: Introductionmentioning

confidence: 99%

“…There are many different experimental approaches to the analysis of cross-linked polymers, such as inverse gas chromatography, osmometry, dynamical mechanical analysis, neutron scattering, or dielectric measurements . However, the most common techniques to determine the cross-link density are mechanical measurements, – NMR spectroscopy, – and equilibrium swelling. – …”

Section: Introductionmentioning

confidence: 99%

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

et al. 2008

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Equilibrium swelling is a feasible and simple experiment to determine the cross-link density of networks. It is the most popular and useful approach; however, in most of the cases, the given values are highly uncertain if not erroneous. The description of the complex thermodynamics of swollen polymer networks is usually based on the Flory-Rehner model. However, experimental evidence has shown that both the mixing term described by the Flory-Huggins expression and the elastic component derived from the affine model are only approximations that fail in the description and prediction of the rubber network behavior. This means that the Flory-Rehner treatment can only give a qualitative evaluation of cross-link density because of its strong dependence on the thermodynamic model. In this work, the uncertainties in the determination of the cross-link density in rubber materials by swelling experiments based on this model are reviewed. The implications and the validity of some of the used approximations as well as their influence in the relationship of the cross-link densities derived from swelling experiments are discussed. Importantly, swelling results are compared with results of a completely independent determination of the cross-link density by proton multiple-quantum NMR, and the correlation observed between the two methods can help to validate the thermodynamic model.

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“…Extension measurements on unswollen rubber were made by Wood and Bullman [19] and by Melley and Stuckey [20]. Compression measurements on swollen rubber were made by Melley and Stuckey and by Redding and Smith [21].…”

Section: Melley and Stuckey [20] • Compressionmentioning

confidence: 99%

Molecular interpretations of modulus and swelling relations in natural rubber cross-linked by dicumyl peroxide

Wood¹

1979

J. RES. NATL. BUR. STAN.

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A survey of published experime ntal work on the modulus of natural rubber cross-linked by di c umyl peroxide permits a compari son with the results and molecular interpretation s obtained in recent NBS work [J . Res. NBS 76A, No.1, 51 (1972), 77A, No.1, 171 (1973) and BOA, No.3, 451 (1976]. Excelle nt agreement was found a mong values of the s hear mod ulus G at the sa me cross-linkin g when the cross-linking is calculated from the a mount of decomposed dic umyl peroxide. The types of de formation includ ed tors ion as well as uniaxial exte nsion a nd compression. G increases linearl y with cross-linking (except at the lowest degrees) with a s lope from 5 to 15 percent greater than that predicted by the simple stati sti cal th eory. Data of Mullins de monst rat ed that at each degree of cross-linking the value of G is int e rm ediate betwee n 2C, and 2(C, + C2 ) where C , and C2 are the Mooney-Rivlin constants . Measure ments of equilibrium swelling at a given degree of cross-linking are in reasonable agreement with each other. However the e ntropy compon e nts of the modulus and the s ub-chain density calc ulated from swelling measure ments are appreciably greater than those calc ulated from cross-li nking or from direct mec hanical measurem e nts. They increase linearly with cross-linking. It is concluded that the number of sub-chains effective in limiting swe lling is greater than that effective in direct mec hani ca l measurement s.Key words: Cross-linki ng of rubber; dicumy l peroxid e; elast ic it y theory of rubber; mod ulu s of nlbbe r; MooneyRivlin constants; rubber e lasti city theory; rubber , natural ; swe lling of nlbber network.. In . IntroductionIn recent yea rs exte nsive investigations have been made of th e mechani cal prope rti es of natural rubber cross-linked by di c umyl pe roxide . Because the basic mec hanism appears to be relatively simple and free from side reactions, this system is particularly suitable for fundamental studies. The amount of cross-linking can readily be calculated from the quantity of peroxide decomposed and not otherwise wasted by reaction with impurities. The calculation assumes that each molecule of unwasted decomposed dicumyl peroxide gives rise to one cross-link. This assumption has found extensive experimental verification in recent years [1][2][3][4][5][6][7][8][9]. I Dicumyl peroxide is thus a quantitative cross-linking agent for natural rubber. It seems quite surprising that with only a few exceptions previous in vestigators have not calculated th e amount of decomposed dicumyl peroxide from the time and te mperature of cure and used it to calculate th e cross-linking. In the present study thi s calc ulation has been mad e utilizing th e times and temperatures of cure reported in the original publi cations.The prese nt paper presents a survey of other published ex perime ntal work in this fi eld and makes a detailed comparison with th e NBS studies. Th e expe rime ntal observations of directly observed quantities show only small disc repancies whi c h can pr...

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A determination of crosslink density from compression modulus data

Cited by 11 publications

References 6 publications

Modulus of natural rubber cross-linked by dicumyl peroxide. III. Some molecular interpretations, possible refinements of theory, and conclusions

Modulus of natural rubber cross-linked by dicumyl peroxide. III. Some molecular interpretations, possible refinements of theory, and conclusions

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

Molecular interpretations of modulus and swelling relations in natural rubber cross-linked by dicumyl peroxide

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