Prediction of Rheological Properties

We now consider predictions of the viscoelastic properties of unentangled polymer melts based on the Rouse model. Consider the situation where a sudden strain is imposed on a polymer. Then the stress remaining in the specimen at time t can be determined from a material property referred to as the stress relaxation modulus G(t). The G(t) for the Rouse model is given by (Doi and Edwards 1986 Rouse 1953) 

Rouse (1953) also derived Eqs. (4.84) and (4.85) from the point of view of the work done on a polymer solution under oscillatory shear flow. 

The Rouse model allows us to determine the stress a contributed by the polymer chains from 

The Rouse model gives the following integral-type constitutive equation (Doi and Edwards 1986) 

In the steady-state shear flow, the Rouse model predicts 

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The flow properties of disordered micellar phases are now reasonably well understood. For spherical micelles the viscosity can be estimated from modified hard-sphere-suspension theories, while for disordered semidilute cylindrical micelles the Cates theory of entangled living polymers provides at least a good starting point, and in some cases nearly quantitative prediction of rheological properties. 

Thin solid films of polymeric materials used in various microelectronic applications are usually commercially produced the spin coating deposition (SCD) process. This paper reports on a comprehensive theoretical study of the fundamental physical mechanisms of polymer thin film formation onto substrates by the SCD process. A mathematical model was used to predict the film thickness and film thickness uniformity as well as the effects of rheological properties, solvent evaporation, substrate surface topography and planarization phenomena. A theoretical expression is shown to provide a universal dimensionless correlation of dry film thickness data in terms of initial viscosity, angular speed, initial volume dispensed, time and two solvent evaporation parameters. 

A more serious deficiency resides in reliance on MFI to characterize different polymers. No single rheological property can be expected to provide a complete prediction of the properties of a complex material like a thermoplastic polymer. Figure 11-27 shows log — log flow curves for polymers having the same melt index, at the intersection of the curves, but very differeni viscosities at higher shear stress where the materials are extruded or molded. This is the main reason why MFI is repeatedly condemned by purer practitioners of our profession. The parameter is locked into industrial practice, however, and is unlikely to be displaced. 

It is interesting to note that equation (11.21) and equivalent expressions for other mixers predict that the laminar mixing action is essentially independent of liquid flow rate and also of rheological properties of the liquid. However, care must be taken in applying these considerations to viscoelastic liquids which tend to resist this type of mixing action... 

Advanced simulation technique that affords predictions of rheology, processing steps, mold filling processes and finished part properties under loads... 

Rheological properties Rheology is the study of the deformation and flow of matter under the influence of an applied stress. The measurement of rheological properties is helpful to predict the physical properties of polymer nanocomposites during and after processing. Oberdisse [44] studied the rheological properties of a special nanocomposite material obtained by film formation of mixtures of colloidal silica and nanolatex solutions by means of uniaxial strain experiments. 

Thermoplastic Melt Rheology and Processing, A. V. Shenoy and D. R. Saini Prediction of Polymer Properties Second Edition, Revised and Expanded, Jozef Bicerano... 

Schrampf E, Leitner E (2010) Prediction of rheological and chemical properties of different starches used in the paper industry by near infrared spectroscopy (NIRS). Macromol Symp 296 154-160... 

The first attempt to predict the rheological properties of the synthetic binders was performed according to the following equation ... 

The knowledge on the stress relaxation progression may be utilized for the prediction of a series of rheological properties of the blend. The plateau modulus, G°, an index of material rigidity, is obtained from (Eq. 14), at the onset of the terminal relaxation region ( = 0) ... 

We have shown in the preceding section that the rheological properties of particulate-filled molten thermoplastics and elastomers depend on many factors (1) particle size (t/p), (2) particle shape (a), (3) volume fraction of filler (f)), and (4) applied shear rate (y) or shear stress a). The situation becomes more complicated when interactions exist between the particulates and polymer matrix. There is a long history for the development of a theory to predict the rheological properties of dilute suspensions, concentrated suspensions, and particulate-filled viscoelastic polymeric fluids. As early as 1906, before viscoelastic polymeric fluids were known to the scientific community, Einstein (1906,1911) developed a theory predicting the viscosity of a dilute suspension of rigid spheres and obtained the following expression for the bulk (effective) viscosity of a suspension ... 

It is clear from the materials presented above that coupling between flow and orientation of fibers is necessary to accurately describe or predict the rheological properties of concentrated suspensions of fibers. Several other research groups (Altan et al. 1989, 1990, 1992 Ranganathan and Advani 1991 Shanker et al. 1991 Shaqfeh and Fredrickson 1990 Tucker and Advani 1974) reported on flow-induced fiber orientation in semicon-centrated or concentrated suspensions closely related to the processing of thermoplastic composite materials. In Chapter 13 of Volume 2 we discuss the importance of fiber orientation in the processing of thermoset/fiber composites. 

Middleman, S., The Flow of High Polymers Continuum and Molecular Rheology , Interscience, New York, 1968. The book discusses three subjects the definition and measurement of material properties, the prediction of these properties and correlation techniques. 

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