Abstract
A theoretical investigation of treating the dependence of viscosity on concentration and molecular weight is carried out by making use of the expression of viscosity obtained from the theory of viscoelasticity in temporarily crosslinked network structure. According to the theoretical equation (1), the viscosity depends not only on the“molecular”length but also on the“chain”length: here the term“molecule”represents the total chain of a molecule, while the term“chain”represents the submolecule between the adjacent crosslinks. Since the chain length depends on concentration, the concentration dependence of viscosity is obtained by investigating the concentration dependence of chain length. It is known from the network theory that the chain length is proportional to C-1 in low concentration, (Eq. 7), and to C-2 in high concentration, (Eq. 8). Accordingly, it is predicted that the viscosity is proportional to M3.5 C3.5 in low concentration range, (Eq. 10), and to M3.5 C6 in high concentration range, (Eq. 12), when the effect of terminal chains is neglected and the friction constant of a segment is assumed to be independent of concentration.
When the effect of terminal chains and the concentration dependence of friction constant of a segment are taken into account, the viscosity is expressed as Eq. (15) in low concentration and as Eq. (16) in high concentration.
Judging from the above results, two kinds of polymer entanglement can be considered; one is the first order entanglement which may result from the overlap of two molecules in low concentration and the other is the second order entanglement which may result from the overlap of more than two molecules in high concentration.
