JOURNAL OF RESEAR CH of the Notion ol Bureo u of Standards - A. Ph ys ics and Chemis tr y V o l. aOA, No. 3, M ay- June 1976 Modulus of Natural Rubber Cross-Linked by Dicumyl Peroxide III. Some Molecular Interpretations, Possible Refinements of Theory, and Conclusions Lawrence A. Wood Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234 (March 6, 1976) Th e shea r modulu s G = 5.925 X 10 - 3(J p - 0.45) T + G* Wa rt I), it s energy co mpon e nt G* = 0.0684 (j jJ - 0.45)+2.70 Wart 11 ), and the numb er of e ffec ti ve s ub-cha in s per unit vo lum e Ve= (G - G*)IRT a re giv en detailed mol ec ul ar considera ti o n. G is give n in Mdyn cm - 2 for rubber cr oss- link ed by a ddin g p part s of dicumyl peroxide per hundr ed of rubb er, and hea ting until a fr ac ti on f of the pero xide is de- compose d. v" is fo und to be a pproximat ely twi ce the density of cross-link s, afte r a co rrec tion for impuri - ties a nd cha in e nd s is made. It ca n not be co mput ed as GI RT, sin ce only the e ntropy co mponent of 1110dulu s is related to li e. Th e s ub -chains for the most highly cross -linked rubb ers studied h ad a mole- c ul ar weight of abou t 575 g 11101 - ', corr es ponding to abo ut 8 iso prene units. Th e modulu s c orres pondin g to no a dd ed cross-links is not zero. It is dete rmin ed chie fiy by the energy c ompo ne nt of the modulu s; it d oes not ar ise from e ntan glements. Th e "front fa ct or " is found to be unit y. An e xt ens iv e lite ratur e survey yi elds valu es of the quantity RN (v,), where \jI (V2) is th e Flory- Rellller e quation function of v" the e quilibrium volume fraction ob tained by swelling the cr oss -linked rubb e r. RT\jI (v,) is found to be greater th an G - G*, but not as lar ge as G it se lf. Key words: Cross- li nk in g of rubb er; di cumyl peroxide; elasticity theory of rub ber: entanglements in rubber; ge l point ; molec ular inter pre tation of rubb er elas ti city; modulu s of rubb er; rubb er el as ti c it y; statistical th eo ry of rubber elasticity; swelling of rubbe r ne t wo rk. 1 . Introduction Th e fir st paper in this se ri es Part I [1] I presented ex pe rimen tal data on th e change of modulus with temperature and cross-linking for natural rubb er cross-linked by dicumyl peroxide, The re sults were prese nt ed in the form of the following e quation: G=S (jp + B)T + H(fp + B) +A = 5.925 X 1O - 3(j p- 0_45) T + 0.0684 (jp-0.45) +2,70 (1.1 ) S, 8, H, and A ar e co ns tant s having the values shown, while G is th e sh ea r modulus (limit of the ratio of s hear s tr ess to st rain at zero deformation, in Mdyn cm -2 or 0.1 MPa) at a te mperature T in kelvin s, for natural rubber cross-link ed by adding p parts of dicumyl pe r- oxide per hundr ed of rubb er (phr) and h eat ing until a fraction f of th e peroxide was d eco mpo se d. Th e actual behavior of th e system at very low degrees of cr oss - I Figur es in brackets in dica te th e lit eratu re references at th e e nd or this paper. linking d eviated from th at give n by the e quation, a nd is discuss ed in a lat er sec ti on of the pre se nt pap er. Th e secon d pap er Part II [2] applied th ermo dynam- ical co nside rations to th e expe rim e ntal results to de- termine th e relative importanc e of G* (= H (jp + B) + A )-the e nergy co mpon e nt of the modulu s-a nd (G - G * )-the entropy component. Th e ex perime ntal entropy component was then compared with that predicted by the statistical theory of rubber elasticity in an extremely simplified presentation. The genera l concepts outlined in the books of Flory [3], Treloar [4], and Ferry [5] were utilized, largely using the form and symbolism employed in the book by Meares [6]. The present pap er makes much mor e detailed molec- ular interpretations of the results than th e seco nd paper and e xamin es th e co nsequ en ces of severa l re fin eme nt s which might be made in th e application of th e th eory, 2. Molecular Interpretations 2.1, The Gel Point The gel point or d egr ee of cross -linking ju st n eces - 451
Modulus of Natural Rubber Cross-Linked by Dicumyl Peroxide III. Some Molecular Interpretations, Possible Refinements of Theory, and Conclusions
Jun 21, 2023
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