A molecular theoretical investigation of the viscoelastic properties of amorphous polymeric substances in the range of long relaxation time has been pursued by using a temporarily crosslinked network model, in which crosslinkages are created by secondary valence of segments or by entanglement of linear polymer molecules.
Consider a single polymer molecule in the system. The deformation of the molecule is different, in general, from that of the system since the polymeric substances do not return to its initial state even though the deformation is removed. Therefore the concept of slipping of molecules or chains is acceptable.
In the present consideration, a part of polymer molecule between two adjacent crosslinkages is termed“chain”, and the chains, each having the same length, are considered to be Gaussian-chain-springs. The friction of chain is replaced by a bead moving in a medium which is the assembly of polymer molecules excepting the said molecule. Therefore a polymer molecule is equivalent to the so-called Rouse model which corresponds to the macro-Brownian motion of molecule contrary to the micro-Brownian motion in the ordinary Rouse model. The medium in this model is viscoelastic medium, since polymer molecules are crosslinked to one another. Therefore one chain in a molecule has elastic and viscous effects on other chains through the agency of the medium. The evaluation of the two effects are made by using the above model and on the following two assumptions. One is the assumption determining the viscous effect and is expressed as “The slipping of a chain is influenced by the contractive force of the chain and by the forces given by the nearest chains”, and the other is the assumption relating to the elastic effect and is written as“In such a motion of polymer molecule that
k chains move in a group, the elastic effect is caused by
k chains”.
From the above model and two assumptions, the slipping equation is obtained in the form of Eq. (26) or Eq. (26') and the stress is expressed by Eq. (28) or Eq. (28'), these two relations show that our model corresponds to the parallel combination of the generalized three dimensional Maxwell model. The relaxation spectrum is of the box type as is given by Eq. (41), in which ν is the number of chains in unit volume,
n is the number of chains in a molecule, and τβ and τα are the maximum and minimum relaxation times of the spectrum. The steady flow viscosity is given by Eq. (43), in which
X and
q are the number of repeating unit in a molecule and in a chain respectively. Eq. (43) shows that the steady flow viscosity is proportional to the 3.4 power of molecular weight. For a system with polydispersed molecular weight distribution, the relaxation time is expressed by Eq. (45), and the“box”is out of shape in the range of long relaxation time.
抄録全体を表示