補強加硫ゴムの静的レオロジー, とくにMullins効果について : 禿ちよろモデル : 高分子固体のレオロジー

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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 a in the direction of z-axis, a portion of the rubbery medium contacted with the point P_0 on the surface of the d-sphere moves to the point P on the surface of a cavity determined by γin 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 a. The transfer of P is caused by the disconnection of adhered chains around the previous position P_0, 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 g_<f0> to the effective one g_f=g_<fo> cosΘunder a constant extension a, let it be assumed that the cap of d-sphere around the z-axis with an area S_0(1-cosΘ), (S_0=2_πd^2) 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 Θ_<j0> and Θ_<j∞> with z-axis be bald as seen in Fig.2. While, when the extended specimen tends to relax, the area S_0cosΘ' of a portion of the spherical surface in contact with the medium within a define 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 γ<II> and also the degree of adhesion (1-ζ) according to the formula γ-1=(γ_<II>-1)ζ. It should be noted that though γ(a(t), t) is the function not only of an extension history a(t) but also a time t, γ_<II> (a(t)) is the function only of a(t), accordingly γ_<II>(a) is an equilibrium quantity under the constant a. If the surface-density g_f=g_f^<(m)>(1-ζ) in the previous theory be approximated by the effective one g_f, an important relation cosΘ=(1-ζ)/(1-ζ_0) is obtained, where g_f^<(m)> denotes the surface-density of perfect adhesion and (1-ζ_0) is given by the virgin density g_<f0>=g_f^<(m)>(1-ζ_0).
1964-05-15

著者

佐藤良泰
信州大学繊維学部

補強加硫ゴムの静的レオロジー, とくにMullins効果について : 禿ちよろモデル : 高分子固体のレオロジー

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