Melt theory, rheology

R. B. Bird, H. H. Saab, and C. F. Curtis. A kinetic-theory for polymer melts. 4. Rheological properties for shear flows. J. Chem. Phys., 77 (1982), 4747-4757. 

However, without theories that explicitly consider the effect of long-chain branching on rheology, we can say nothing beyond affirming that the samples contain LCB. In what follows, we will describe some recently developed theories for predicting the linear viscoelasticity of long-chain-branched polymer melts. Theories for the nonlinear viscoelasticity of branched polymers are covered in Section 11.6. 

The above considerations illustrate the difficulties of trying to formulate equations descriptive of rheological behavior of polymer melts with gas bubbles. An optimistic approach to the solution of this task is contained in [60, 61]. The content of these works is revealed by their titles On the Use of the Theory of Viscoelasticity for Describing of the Behaviour of Porous Material and for the Calculation of construction... 

As we conjectured in the introduction, the fundamental role of topology in this approach to entangled polymer dynamics would indicate that changes to the topology of the molecules themselves would radically affect the dynamic response of the melts. In fact rheological data on monodisperse star-branched polymers, in which a number of anionically-polymerised arms are coupled by a multifunctional core molecule, pre-dated the first application of tube theory in the presence of branching [22]. Just the addition of one branch point per molecule has a remarkable effect, as may be seen by comparing the dissipative moduli of comparable linear and star polymer melts in Fig. 5. 

Theory for block copolymer rheology is still in its infancy. There are no models that can predict the rheological behaviour of a block copolymer from microscopic parameters. Fredrickson and Helfand (1988) considered fluctuation effects on the low frequency linear viscoelastic properties of block copolymers in the disordered melt near the ODT. They found that long-wavelength transverse momentum fluctuations couple only to compositional order parameter fluctua-... 

M. H. Wagner and J. Schaeffer, Constitutive Equations from Gaussian Slip-link Network Theories in Polymer Melt Rheology, Rheol. Acta, 31, 22-31 (1992). 

Cooke BJ, Matheson AJ (1976) Dynamic viscosity of dilute polymer solutions at high frequencies of alternating shear stress. J Chem Soc Faraday Trans II 72(3) 679-685 Curtiss CF, Bird RB (1981a) A kinetic theory for polymer melts. I The equation for the single-link orientational distribution function. J Chem Phys 74 2016—2025 Curtiss CF, Bird RB (1981b) A kinetic theory for polymer melts. II The stress tensor and the rheological equation of state. J Chem Phys 74(3) 2026—2033 Daoud M, de Gennes PG (1979) Some remarks on the dynamics of polymer melts. J Polym Sci Polym Phys Ed 17 1971-1981... 

Among the various approaches in use for the depiction of the interactions of the polymer molecules in the melt, these being known to be at the origin of the observed rheological behaviour, the network theories enable the building of reasonable models that fulfill the previous requirements for the sake of simplicity. 

M.H.Wagner, J.Schaeffer, Constitutive equations from Gaussian slip-link network theories in polymer melt rheology, Rheol. Acta 31 (1992), 22-31. 

Dealy, J. M. and Wissbum, K, F. 1990. Melt Rheology and Its Role in Plastics Processing Theory and Applications, Van Nostiand Reinhold, New York. 

There is much more to tell about the rheology of filled melts, but space limitations preclude further discussion here. The interested reader is directed to the articles by Khan and Prud homme (1987), Metzner (1985), amd White (1982), the book by Han (1981), and references therein. Viscoelastic theories for filled melts, especially for rubbers containing carbon black, can be found in Montes and White (1993), Witten et al. (1993), and references therein. 

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