The theory of polymer dynamics

OTHER RELAXA nON MODES 237 relaxation time, which no viscoelastic data seem to support Curtiss and Bird54 suggested that the segmental friction constant ~ may depend on the molecular weight, but this hypothesis seems to contradict the result of the diffusion experiment Another possibility suggested by Ba1l55 takes into account the long-range correlation in the motion of vacancies needed for the reptation motion to take place This has been studied by computer simulation,56 but the result is not yet conclusive At present, a more consistent explanation seems to be that given by Graessley,36 who pointed out that the observed viscosity and the relaxation time are smaller than the calculated ones Using egns (7.32), (7.33), (7.46), and (7.47), one can show that 238 MOLECULAR THEORY OF POLYMERIC LIQUIDS any relaxation process which occurs concurrently with reptation decreases the viscosity and hence reduces the discrepancy between the theory and experiment 7.4.2 Contour length fluctuation and tube reorganization Two relaxation processes have been suggested to alter the pure reptation behaviour discussed in Section 7.3.3 Fig 7.8 Release and creation of the topological constraints (a) The topological constraints imposed on the chain A by C is released and recreated by the motion of C (b) In the two-dimensional representation, this process can be represented by the disappearance and reappearance of the obstacle C The process causes the deformation of the tube in the middle still at the level of conjecture, and there are other theoretical treatments.62,63Experimentally, in linear polymers with narrow molecular weight distribution, it seems that the major difficulty of the theory can be resolved by induding the contour length fluctuation On the other hand the tube reorganization is believed to be important for polymers with broader molecular weight distribution,60 or long branches, which will be discussed later 7.5 Stress relaxation after large step strain 7.5.1 Experimental setup Having seen the characteristic features of the linear viscoelasticity, we shall now study the nonlinear viscoelasticity Before studying the general situation, we shall first consider a simple case, the stress relaxation after stepwise deformation.14,64 Suppose that at time t = 0, a polymeric liquid is suddenly deformed homogeneously The deformation creates a stress which gradually relaxes with time Our problem is to find how this relaxation takes place For a homogeneous deformation, we may assume without loss of Though the elastic energy equation (10.140) is important in many nonlinear flow properties of low-molecular-weight nematics, its effect is less important in polymeric nematics since the stress is usually dominated by the viscosity in polymeric nematics Polymeric nematics often take up a certain domain structure at equilibrium.45,46 Various patterns have been observed by polarization microscopy Curiously enough, such structures seem to correspond to the minimum of free energy since even after the system is brought to a homogeneous state by shearing, the domain structure is spontaneously recovered when the flow is stopped.47 The formation and destruction of the domain structure are quite important in the macroscopic flow properties, and indeed dominate the phenomena at low stress level At present, however, the physical origin of the domain structure is not known and the flow properties at low stress levels are poorly understood.48 10.6.3 Thermotropic liquid crystals Much of the current research on polymeric liquid crystals is directed towards thermotropic liquid crystals3-5 which are formed when certain polymer melts are cooled Many of those polymers includes chemical groups similar to low-molecular-weight nematics either along the main chain or in the side chains These materials are technologically interesting because of their ease of processing Theoretically, these materials are expected to show curious behaviours which are a mixture of their ... by the motion of C (b) In the two-dimensional representation, this process can be represented by the disappearance and reappearance of the obstacle C The process causes the deformation of the. .. for the contraction of the contour length Various reasons for this behaviour are conceivable such as the limited range of the scattering wave vector or polydispersity of the sample On the other... other hand the results may indicate the importance of the tube deformation in the nonequilibrium state.80 Theoretical calculations of the scattering intensity based on the reptation dynamics are