faster diffusion of the latter. Hence, the local constraint on the tube shape confining
the long chain is released, which is calledthermal constraint release(TCR).
Therefore, in a polydisperse system, the diffusion coefficients of long-chain
fractions are highly related to the short-chain fractions, and the polydispersity
affects the chain motion of polymers (Graessley 1982 ). After the thermal constraint
release, the distance between two neighboring entanglement points along the chain
is increased. Therefore, the corresponding radius of the local tube is enlarged
(Milner and McLeish 1997 ). Such a situation is often calleddynamic tube dilation
(DTD). The DTD model can be applied to the chain dynamics of long-chain-
branching polymers like star-shape polymers. Since the branching point diffuses
relatively slowly, thearm retraction(AR) can be further considered on the basis of
the Rouse-chain model. The characteristic relaxation time of long-chain branches is
extremely long, and the viscosity does not rely on the number of arms, but rather,
exponentially on the length of arms. Once the whole polymer is stretched,
its retraction becomes extremely difficult, which is a phenomenon known as
extensional-hardening(McLeish 2002 ). The details of theoretical treatments can
be found from the literature mentioned above. More challenges still remain,
regarding the influence of chain rigidity, nano-confinement, heterogeneous
phases and charge interactions on the chain dynamics, which are prevailing in
bio-macromolecules and playing important roles in various living processes.
Question Sets
- Why do we say that the Rouse-chain model rests on the ideal-chain model?
- Why does the Zimm chain run faster than the Rouse chain?
- Why can the reptation-chain model describe the Brownian motions of long-
chain polymers? - Why do polymers have a rubber plateau between the glass state and the liquid
state? - What are the characteristics of branched-chain motions?
References
Colby R, Fetters LJ, Graessley WW (1987) Melt viscosity - molecular weight relationship for
linear polymers. Macromolecules 20:2226–2237
De Gennes PG (1971) Reptation of a polymer chain in a presence of fixed obstacles. J Chem Phys
55:572–579
Des Cloizeaux J, Jannink G (1990) Polymers in solution: their modelling and structure. Oxford
University Press, Oxford
Doi M (1983) Explanation for the 3.4 power-law for viscosity of polymeric liquids on the basis of
the tube model. J Polym Sci Polym Phys 21:667–684
Edwards SF (1967) The statistical mechanics of polymerized material. Proc Phys Soc 92:9–13
Einstein A (1905) Investigations on the theory of the Brownian movement. Ann Phys (Leipzig)
17:549–560
Einstein A (1911) Eine neue Bestimmung der Molekuldimensionen. Ann Phys (Leipzig)
34:591–592
90 5 Scaling Analysis of Polymer Dynamics