Thermorheological behavior

To transform a polymer rapidly into a useful product, the molten polymer is often cooled while it flows, for example, into a mold or from a die. Modeling of these thermoshaping 

T 10 /° vkpT / o were observed at cr =20 MPa from their orientation, the Mohr-Coulomb 

Here the dependence of aj on the free volume Vf allows none to be captured, so that the material time depends on the thermal history and not just the instantaneous temperature. Use of a material clock similar to this can be recognized in 

Such residual stresses lead to warping, anisotropic shrinkage, and other product flaws. Thus, adequate thermorheological modeling remains a major engineering problem. 

Of these models, the mode-coupling theory has the clearest direct coimection to liquid-state structure it attempts to describe nonhnear density fluctuations in dense liquids. 

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Liao, H.-J. 1998. Simulation of continuous sterilization of fluid food products the role of thermorheological behavior of starch dispersion and process, Ph.D. thesis, Cornell University, Ithaca, NY. 

Liao, H.-J., Rao, M. A., and Datta, A. K. 2000. Role of thermorheological behavior in simulation of continuous sterilization of a starch dispersion. iChemE Trans. Part C—Food and Bioproducts Process. 78(C1) 48-56. 

The existence of ion clustering in perfluorinated sulfonate ionomers was first reported by Yeo and Eisenberg in 1975. This phenomenon has been subsequently studied for perfluorinated sulfonate and carboxylate ionomers by many Experimental evidence to support the conclusion that ion clustering occurs in these materials includes thermorheological behavior/ X-ray diffraction results/" " " IR data/ " NMR data,"" " ESR data/ Mossbauer spectroscopic fluores-... 

G.C. Reichart, W.W. Graessley, R.A. Register, D.J. Lohse, Thermodynamics of mixing for statistical copolymers of ethylene and a-olefins. Macromolecules 31(22), 7886-7894 (1998) J. A. Resch, U. KeBner, F. J. Stadler, Thermorheological behavior of polyethylene a sensitive probe to molecular structure. Rheol. Acta 50, 559-575 (2011)... 

Wood-Adams, P, Costeux, S. Thermorheological behavior of polyethylene Effects of micro-structure and long chain branching. Macromol (2001) 34, pp. 6281-6290... 

One should note that the Arrhenius and WLF equations do not always fit to determine rheological behavior of a polymer even in vicinity of Tg. Besides, the mode of mechanical stress has an influence on the thermorheological behavior (63). 

The rheological properties of insitu polymerized nanocomposites with end-tethered polymer chains were first described by Krisnamoorti and Giannelis [33]. The flow behavior of PCL- and Nylon 6-based nanocomposites differed extremely from that of the corresponding neat matrices, whereas the thermorheological properties of the nanocomposites were entirely determined by the behavior of the matrices [33]. The slope of G (co) and G"(co) versus flxco is much smaller than 2 and 1, respectively. Values of 2 and 1 are expected for linear mono-dispersed polymer melts, and the large deviation, especially in the presence of a very small amount of layered silicate loading, may be due to the formation of a network structure in the molten... 

Many amorphous homopolymers and random copolymers show thermorheologically simple behavior within the usual experimental accuracy. Plazek (23,24), however, found that the steady-state viscosity and steady-state compliance of polystyrene cannot be described by the same WLF equation. The effect of temperature on entanglement couplings can also result in thermorheologically complex behavior. This has been shown on certain polymethacrylate polymers and their solutions (22, 23, 26, 31). The time-temperature superposition of thermorheologically simple materials is clearly not applicable to polymers with multiple transitions. The classical study in this area is that by Ferry and co-workers (5, 8) on polymethacrylates with relatively long side chains. In these the complex compliance is the sum of two contributions with different sets of relaxation mechanisms the compliance of the chain backbone and that of the side chains, respectively. 

Since the relaxation mechanisms characteristic of the constituent blocks will be associated with separate distributions of relaxation times, the simple time-temperature (or frequency-temperature) superposition applicable to most amorphous homopolymers and random copolymers cannot apply to block copolymers, even if each block separately shows thermorheologically simple behavior. Block copolymers, in contrast to the polymethacrylates studied by Ferry and co-workers, are not singlephase systems. They form, however, felicitous models for studying materials with multiple transitions because their molecular architecture can be shaped with considerable freedom. We report here on a study of time—temperature superposition in a commercially available triblock copolymer rubber determined in tensile relaxation and creep. 

In an earlier section, we have shown that the viscoelastic behavior of homogeneous block copolymers can be treated by the modified Rouse-Bueche-Zimm model. In addition, the Time-Temperature Superposition Principle has also been found to be valid for these systems. However, if the block copolymer shows microphase separation, these conclusions no longer apply. The basic tenet of the Time-Temperature Superposition Principle is valid only if all of the relaxation mechanisms are affected by temperature in the same manner. Materials obeying this Principle are said to be thermorheologically simple. In other words, relaxation times at one temperature are related to the corresponding relaxation times at a reference temperature by a constant ratio (the shift factor). For... 

Few examples of the homogeneous diblock-incompatible homo-polymer behavior have been reported. One that has received considerable attention is the system polystyrene-poly-a-methylstyrene (2). Block copolymers of styrene and a-methylstyrene exhibit a single loss peak in dynamic experiments (2,3) and have been shown to be thermorheologi-cally simple (4) hence they are considered to be homogeneous. Mechanical properties data on these copolymers also has been used to validate interesting extensions of the molecular theories of polymer viscoelasticity (2,3,4). 

In order to understand or study heat transfer phenomenon, the rheological behavior of a fluid food must be known as a function of both temperature and shear rate. For convenience in computations, the effect of shear and temperature may be combined in to a single thermorheological (TR) model. A TR model may be defined as one that has been derived from rheological data obtained as a function of both shear rate and temperature. Such models can be used to calculate the apparent viscosity at different shear rates and temperatures in computer simulation and food engineering applications. For a simple Newtonian fluid, because the viscosity, r), is independent of shear rate, one may consider only the influence of temperature on the viscosity. For many foods, the Arrhenius equation (Equation 2.42) is suitable for describing the effect of temperature on t] ... 

Lest one ignore the important role of rheological behavior and properties of fluid foods in handling and processing foods, they are covered in Chapter 8. Here, the topics covered include applications under isothermal conditions (pressure drop and mbcing) and under non-isothermal conditions (heat transfer pasteurization and sterilization). In particular, the isothermal rheological and nonisothermal thermorheological models discussed in Chapters 3 and 4 are applied in Chapter 8. 

Freitas LD, Burgert J, Stadler R (1987) Thermoplastic elastomers by hydrogen-bonding. 5. Thermorheologically complex behavior by hydrogen-bond clustering. Polym Bull 17 (5) 431 38... 

See the discussion on thermorheological simplicity in Chapter 26 on Viscoelastic Behavior. 

A very simple result is obtained if thermorheologically simple behavior is imposed on this mechanical model as an additional restriction. In this case, all spring constants of the model are temperature-independent while the viscosities all have a similar temperature dependence. By a change from the temperature T to the... 

Thermorheologically complex behavior is shown in Figure 21 where the temperature dependencies for segmental (relaxation times) and chain (shift factors) dynamics are compared for atactic polypropylene. For both processes, different methods are combined. 

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