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

Wood, Lawrence A.

doi:10.6028/jres.080a.051

Cited by 8 publications

(12 citation statements)

References 52 publications

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“…Figure 1 of the present paper is a plot of the data of Tamura and Murakami [18] in extension for another comparison with the straight line representing eq. [12] the observed values of G at low degrees of cross-linking fall below the line. Values shown for fp (lower abscissa scale) are based on the application of eqs (2.2) and (2.3) to the curing conditions specified by the authors.…”

Section: Modulus and Cross-linkingmentioning

confidence: 98%

“…The previous paper [12] concluded that any differences among the remaining 23 reports of experimental results were small and could probably be explained in terms of minor differences in the specimens.…”

Section: Swelling and Cross-linkingmentioning

confidence: 99%

“…An extensive literature survey in Part III [12] has considered 28 published papers reporting values of equilibrium swelling volume as a function of cross-linking for the dicumyl peroxide system.…”

Section: Swelling and Cross-linkingmentioning

confidence: 99%

“…In prev ious studies at th e NBS, ex perimental observations, Part I [10], were compared with theory, Part II [11], and given a more detail ed mol ecular interpretation, Part III [12].…”

Section: Introductionmentioning

confidence: 99%

“…Th e expe rime ntal observations of directly observed quantities show only small disc repancies whi c h can probably be ex plained simply in te rms of differences in purity or molecular we ight of the rubber. A muc h wider variation exists with respec t to calculated molec ular quantities, partic ularly the calc ulated numbe r of effectiv e sub-c hains .In prev ious studies at th e NBS, ex perimental observations, Part I [10], were compared with theory, Part II [11], and given a more detail ed mol ecular interpretation, Part III [12].1 Figures in brac kets indi cate lit e rature refe re nces at the end of this paper. …”

mentioning

confidence: 99%

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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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Section: Modulus and Cross-linkingmentioning

confidence: 98%

Section: Swelling and Cross-linkingmentioning

confidence: 99%

Section: Swelling and Cross-linkingmentioning

confidence: 99%

“…In prev ious studies at th e NBS, ex perimental observations, Part I [10], were compared with theory, Part II [11], and given a more detail ed mol ecular interpretation, Part III [12].…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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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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Temperature and crosslinking effects on the swelling of poly(isoprene) in isopiestic conditions

McKenna

Crissman

1997

J. Polym. Sci. B Polym. Phys.

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Isopiestic measurements of solvent uptake have been made in the synthetic isoprene/benzene system for both crosslinked and uncrosslinked polymers in order to revisit the question of the swelling activity parameter S. Both the nonzero value of S at zero swelling and the appearance of a peak in S vs. degree of swelling have been observed in some solvent/rubber pairs and we here investigate both the crosslink and temperature dependencies of these phenomena. The data analysis is an extension of prior work from this laboratory using continuum thermodynamics concepts and avoiding molecular models in an attempt to establish the fundamental phenomenology of the process and the validity or lack of validity of the hypothesis that the mixing and elastic contributions to the free energy of networks are separable. We present results from measurements in benzene vapors at temperatures between 10 and 55°C for an uncrosslinked rubber and rubbers crosslinked with 1, 5, 10, and 15 parts per hundred dicumyl peroxide. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 817–826, 1997

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Elasticity, Rubber‐like

Queslel

Mark

2001

Encyclopedia of Polymer Science and Technology

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Long, flexible polymer chains with high mobility and weak interchain interactions may be covalently linked together to form network structures. These materials exhibit a unique behavior called rubber‐like elasticity, which is high and reversible deformability (up to 10 times the original dimension). The origin of elasticity at thermodynamic equilibrium is the decrease in entropy of the chains between cross‐linking points resulting from the extension. Elastomers therefore follow thermodynamic laws similar to those for gases. There is a minor intramolecular energetic component in the retractive force which can be extracted from thermoelasticity experiments and is related to conformational energy changes of the chains. Most of the theoretical and experimental works in the field of rubber‐like elasticity have been devoted to the characterization of network structures. Molecular models based on statistical mechanics have been applied to the analysis of equilibrium properties such as stress–strain measurements in uniaxial extension and swelling by a solvent. The real behavior of rubbers is between the predictions of the simple affine and phantom models and is well represented by molecular models which include entanglement constraints. These models associated with topological descriptions of networks are powerful tools to describe network structures.

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

Cited by 8 publications

References 52 publications

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

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

Temperature and crosslinking effects on the swelling of poly(isoprene) in isopiestic conditions

Elasticity, Rubber‐like

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