Polymer Viscoelasticity: Basics, Molecular Theories, by Yn-Hwang Lin
By Yn-Hwang Lin
This publication covers in nice aspect the Rouse-segment-based molecular theories in polymer viscoelasticity - the Rouse conception and the prolonged reptation thought (based at the framework of the Doi-Edwards conception) - which were proven to provide an explanation for experimental ends up in a constantly quantitative manner. the reason for the 3.4 strength legislation of viscosity, quantitative line-shape analyses of viscoelastic responses and agreements among different types of viscoelastic responses, the consistency among the viscoelasticity and diffusion effects, the rationalization of the onset of entangelement, the invention of the variety of entanglement strands in line with cubed entanglement distance being a common consistent and the fundamental mechanism of the glass transition-related thermorheological complexity are mentioned or proven in nice aspect. The secret in the back of the good fortune of the Rouse-segment-based molecular theories over the entropic zone of a viscoelastic reaction is printed via the Monte Carlo simulations at the Fraenkel chains. in particular, the simulation experiences provide a traditional cause of the coexistence of the energy-driven and entropy-driven modes in a viscoelastic reaction and supply a theoretical foundation resolving the anomaly that the experimentally decided sizes of Rouse and Kuhn segments are approximately an identical. This e-book starts off from a truly primary point; every one bankruptcy is equipped upon the contents of the former chapters. hence, the readers may possibly use the booklet as a textbook and finally achieve a complicated examine point. This ebook can be an invaluable resource of reference for physicists, chemists and fabric scientists.
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Extra info for Polymer Viscoelasticity: Basics, Molecular Theories, Experiments and Simulations
The probability of ﬁnding the particle in the region, x → x + dx, is denoted by p(x) dx. Since a point does not have a width, it takes a special consideration to describe the state that the particle is surely at a certain point x . From such a consideration, the Dirac delta function δ(x − x ) is obtained. A simple way is to consider the probability function p(x) given by p(x − x ) = 1 =0 for |x − x | ≤ otherwise. 1) August 18, 2010 18:19 WSPC/Book Trim Size for 9in x 6in b959-ch01 Polymer Viscoelasticity 14 It is clear that Eq.
Thus, corresponding to Eq. 28) where C is just a constant. If there are n particles in the container and the interactions among the particles can be ignored because the gas is very dilute, the total entropy is S = k ln(V n ) + nC = nk ln(V ) + nC. 30) which is the ideal gas law and is equivalent to Eq. 22) for the ideal rubber. The basic physical eﬀect responsible for rubber elasticity can be applied to any length of polymer chain which is suﬃciently long. In a polymeric liquid, whose concentration is high and whose polymer chains are long, entanglements between polymer chains can occur.
The basic physical eﬀect responsible for rubber elasticity can be applied to any length of polymer chain which is suﬃciently long. In a polymeric liquid, whose concentration is high and whose polymer chains are long, entanglements between polymer chains can occur. As we shall see in Chapters 8–12, an entanglement can be treated as an impermanent crosslink. Chain slippage through entanglement links will occur to equilibrate the uneven segmental distribution caused by the applied deformation. Before the chain slippage mechanism has a chance to take place after a step deformation is applied, the entanglement links can be regarded as ﬁxed; the measured modulus (in the linear region) can be used to calculate the entanglement molecular weight Me by using Eq.