抄録
In applications of a previously reported theory to a preliminary study about rheological characteristics of the filler-reinforced rubber vulcanizate, an analysis of abnormally large hystersis loops in extension cycles has been attempted here, based on a simple assumption for the rate of change in the adhered state between the filler and the chain molecules of the rubbery medium. In the previous model in Fig. 2, as soon as the specimen is extended to an extension ratio α in the direction of z-axis, a portion of the rubbery medium contacted with the point P0 on the surface of the dsphere moves to the point P on the surface of a cavity determined by γ in the previous theory, and then the portion P moves gradually toward the limit position P∞ on the surface of an equilibrium cavity γ∞ determined by α. The transfer of P is caused by the disconnection of adhered chains around the previous position P0, and when the strain energy of the medium is exhausted owing to the disconnection, P tends to the terminus P∞. When the disconnection proceeds from the original surface-density of adhered chains gf0 to the effective one gf=gf0 cosΘunder a constant extension α, let it be assumed that the cap of d-sphere around the z-axis with an area S0(1-cosΘ), (S0=2πd2) is growing bald like an egg, as seen in Fig. 2. In j th course of the extension cycle, let the zone of d-sphere located between the two small circles which are placed at respective angle Θj0 and Θj∞ with z-axis be bald as seen in Fig. 2. While, when the extended specimen tends to relax, the area S0cosΘ' of a portion of the spherical surface in contact with the medium within a definite small distance increases, and the quick readhesion in a portion of the disconnected chains is possible within this area; perhaps most of the physical adhesions and some of chemical ones may be readhered. From the previous theory, the size of a cavity γ is determined by that of perfect non-adhesion γII and also the degree of adhesion (1-ζ) according to the formula γ-1=(γII-1)ζ. It should be noted that though γ(α(t), t) is the function not only of an extension history α(t) but also a time t, γII(α(t)) is the function only of α(t), accordingly γII(α) is an equilibrium quantity under the constant α. If the surface-density gf=gf(m)(1-ζ) in the previous theory be approximated by the effective one gf, an important relation cosΘ=(1-ζ)/(1-ζ0) is obtained, where gf(m) denotes the surface-density of perfect adhesion and (1-ζ0) is given by the virgin density gf0=gf(m)(1-ζ0).
Based on this picture, let us assume the rate of disconnection, [d(1-ζj)/dt]d, and that of read-hesion, [d(1-ζj)/dt]r, in jth course of extension cycles is described respectively as following schema:
[d(1-ζj)/dt]d_??_{the area of a zone S0(cosΘj-cosΘj∞) of d-sphere}
×{the size of a cavity (γII-1) of the perfect non-adhesion
under an instantaneous value of α(t)}, (Eq. (3.2) cf.)
