Polymer Melt Rheology

You may have heard the expression as slow as molasses in February (or was it January ), referring to the fact that this byproduct of refining sugar (called treacle 

The story of the Great Molasses Flood (it s true, you can t make up stuff like that) is a useful introduction to our discussion of the viscosity of polymer melts, because 

FIGURE 13-58 The great Boston molasses disaster (Courtesy AP/WIde World Photos). 

13-59 is established. Newton made the plausible assumption that the rate of deformation of the fluid, the strain rate, is proportional to the shear stress applied, but the motion is resisted by what he called the lack of slipperiness of the parts of the liquid, what we now call the viscosity. 

A perfectly elastic solid subjected to a non-destructive shear force will deform almost instantaneously an amount proportional to its shear modulus and then deform no further, strain energy being stored in the bonds of the material. A fluid, on the other hand, continues to deform under the action of a shear stress, the energy imparted to the system being dissipated as flow. 

Consider any dynamical system that can be characterized by an input a(t) and an output b(t), where a and b are functions of the independent variable, which we will assume is time. The input is often called the forcing function, and the output the response. The system is linear if the following criterion is satisfied  

It further follows from this relation that 

input o i 7i(f) + aiaift) -------1- o-jvfljvCO output aibifl) + aibiif) -----h 

Integration and differentiation are linear operations, so processes described by linear differential and integral equations are linear dynamical systems. 

An autonomous linear system is one in which all system parameters are independent of time, and integrals that exist in the system description are of convolution type (a convolution integral has the form/o° f t- t )a t )dt ). It is readily 

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F. N. Cogswek, Polymer Melt Rheology, Halsted Press, a division of John Wiley Sons, Inc., New York, 1981, p. 40. 

COGSWELL, p. N., Polymer Melt Rheology, Geo. Godwin, London (1981)... 

Cogswell FN (1981) Polymer melt rheology a guide for industrial practice. Woodhead, Cambridge... 

M. J. McCarthy, R. L. Powell 2001, (Polymer melt rheology by magnetic resonance imaging), Macromolecules 34, 5520. 

H. Janeschitz-Kreigl, Polymer melt rheology and flow birefringence, Springer/Ver-lag (1983). 

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

H. Janeschitz-Kriegl, Polymer Melt Rheology and Flow Birefringence, Springer-Verlag, Berlin 1983. 

Ewen B, Maschke U, Richter D, Farago B (1994) Neutron spin echo studies on the segmental diffusion behaviour in the different chain sections of high molecular weight poly(dimetylsiloxane) melt. Acta Polym 45 143-147 Faitelson LA (1995) Some aspects of polymer melts rheology. Mech Compos Mater 31(1) 101—116... 

This term varies significantly with the nature of the fuel. Liquid fuels are characterized by the presence of recirculation currents induced by buoyancy. These currents homogenize the temperature distributions, reducing in-depth conduction. Nevertheless, convective motion transfers heat to the interior of the pool leading to an additional term of in-depth convection. Convective heat transfer in polymer melts has a similar behavior and could potentially have an important effect on burning rates nevertheless, the impact of polymer melt rheology on the flammability of materials is still a matter of great controversy. 

Janeschitz-Kriegl H, "Flow-birefringence of elasto-viscous polymer systems", Adv Polym Sci, 6 (1969) 170. Janeschitz-Kriegl H, "Polymer Melt Rheology and Flow Birefringence", Springer Verlag, New York, 1983. 

F. N. Cogswell, Polymer Melt Rheology. Woodhead Publishing, Cambridge, England, 1997. J. M. Dealy, Rheometers for Molten Plastics. Van Nostrand Reinhold, New York, 1982. 

One convenient strategy to interpret these results is to review the molecular characteristics of binary blends as extracted from polymer melt rheology [40]. The influence of short chains (M < Me) is to effectively decrease the plateau modulus and the terminal relaxation times as compared to the pure polymer. Consequently, the molecular weight between entanglements... 

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

The appearance of extrusion defects eind instabilities [1-3] in polymer melts flowing through sudden contractions is usuedly related to fluid slip at the wall [4, 5]. It is therefore understandable that this phenomenon has been widely investigated in many studies. However, it is importeint to start with, to note the existence of various types of slip. In the field of polymer melt rheology, the following are referred to ... 

Israelachvili JN(1992). Intermolecular and Surface Forces, 2nd ed, Academic Press, New York. Janeschitz-Krieg] H (1983). Polymer Melt Rheology and Flow Birefringence, Delft University Press. 

FN Cogswell. Polymer Melt Rheology. New York John Wiley Sons, Inc. 1981. 

Tadmor, Z. Gogos, C.G. Polymer melt rheology. In Principles of Polymer Processing John Wiley Sons, 1979 148-172. 

Fig. 1 A schematic comparison between polymer melt rheology and colloid rheology, (a) In a polymer melt, atypical chain (dashed curve) is constrained by many (in reality, 10 ) other chains, here represented by small circles. This gives rise to the fruitful mean-field concept of a tube in which the chain has to move, (b) In a concentrated colloidal suspension, a typical particle (hatched) is surrounded (in 3D) by 10 neighbours. This number is too small for mean-field averaging to be meaningful, (c) Large deformations in polymer melts, such as the process (i) -(ii), involves breaking covalent bonds, and so do not ordinarily occur, (d) There are no covalent constraints on order unity deformations, such as (i)—>(ii), in a colloidal suspension...

Kroger, M., NEMD computer simulation of polymer melt rheology. RheoL, 5, 66-71, 1995. 

Royer, J.R., et al.. Polymer melt rheology with high-pressure C02 using a novel magnetically levitated sphere rheometer. Polymer, 2002. 43(8) p. 2375-2383. 

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