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

Abstract

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...

Effect of the Cross-Linking Density on the Swelling and Rheological Behavior of Ester-Bridged β-Cyclodextrin Nanosponges

“…This may be as a consequence of the number of added effective sub-chains calculation from the number of added cross-links. Taken together, this highlights the assumption that two effective sub-chains are equally with each added cross-link [87]. At this stage it is not possible to fully explain the gap between the values of cross-linking density, as it may arise both from the experimental procedure used to prepare the gels and from the intrinsic differences between the two models applied.…”