Polymer Melt Rheology A For Indu
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Recent advances in analytical rheology for all the different kinds of complex fluids are too broad a topic to cover adequately. Hence, in this paper, we will focus on a particularly important class of complex fluids, namely, polymer melts, which have seen tremendous progress in both rheological modeling and analytical rheology, over the past 30 years. In addition, purely in terms of commercial impact, polymers are among the most important members of the complex fluids family.
In an industrial setting, this dichotomy of SCB and LCB is helpful, since the levels of both types of branching can be independently adjusted to control rheology (important for melts during processing) and crystallinity (important for ultimate solid-state properties), independently.
I will review the specific advantages of analytical rheology of LPs and BPs in the next section. I will then present a brief summary of different molecular models used to study polymer dynamics and rheology and argue why the tube model is an attractive candidate as the rheological model to invert. For LPs, I will focus on the inversion of linear viscoelastic spectra to reconstruct the molecular weight distribution and point out the different techniques and challenges. For BPs, I will review different experimental and model-driven methods to infer the level of LCB from linear and nonlinear viscoelastic measurements. This material is covered in Section 4.
A second important factor in favor of rheology is its sensitivity to the high molecular weight tail of the distribution, which is often important to characterize accurately, because of its outsized influence on processability. The sensitivity of rheology to molecular weight is unparalleled. For example, doubling the molecular weight of a moderately entangled LP causes the zero-shear viscosity to increase approximately 10-fold. For a similar doubling of the arm-molecular weight of a symmetric star polymer, the zero-shear viscosity increases a dramatic 1000-fold. In contrast, the molecular weight dependence of SEC () and light scattering () are much weaker. The dependence of other linear and nonlinear material functions on molecular weight is also quite pronounced. This strong dependence can, in principle, be directly translated into analytical sensitivity and resolution, especially at higher molecular weights where competing analytical methods are particularly ill-suited [54, 60, 61].
From an industrial standpoint, perhaps no other driving force is as important as cost. Here too, rheology has an important advantage over chromatography; it typically costs only about a third of the cost of SEC . In addition to these obvious advantages, carrying out routine linear viscoelastic measurements has simultaneously become more routine and accurate, enabling nonexperts to perform experiments competently. Consequently, analytical rheology of LPs has made its way into some commercial rheometers.
Thus, today, breakthroughs in catalyst technology have allowed us to produce industrial quantities of polymers with precisely controlled molecular structure [64, 65]. However, these advances in chemistry have not been accompanied by simultaneous advances in the characterization of LCB. We are left with a situation where the resolution of standard analytical tools available for diagnosing LCB is much lower than our ability to synthesize sparse levels of precisely controlled branching. The need to develop analytical methods to accurately detect and quantify these trace levels of LCB has become increasingly urgent, and analytical rheology has emerged as a particularly promising candidate .
In this section, we present a historical record of the modeling of polymer melt rheology before considering the most popular ansatz, namely, the tube model, more closely. The tube model and its modifications are ideally suited for inversion using analytical rheology because they offer a reasonable mix of accuracy and efficiency. We will end this section with a brief remark about other more accurate, but computationally intensive, methods for modeling polymer dynamics and rheology. In the future, with faster computers and better algorithms, it is conceivable that some of these models could serve as the forward model.
The unusual sensitivity of rheology to molecular structure makes it an attractive candidate as a tool for inferring structure from simple rheological measurements, where the sensitivity is translated into resolution of the analytical tool. This typically requires the inversion of a forward model (as shown in Figure 1), which may be a simple correlation or empirical thumb-rule (e.g., indices to infer LCB), a simplified toy version of a more complicated model (e.g., use of simple double-reptation-type models for inferring the molecular weight distribution of LPs), simplified applications of incomplete models (e.g., use of pom-pom model to map the nonlinear rheology of complex BPs), or a full-blown sophisticated model capable of handing arbitrary mixtures of polymers of arbitrary mixtures (e.g., hierarchical models for linear viscoelasticity such as BoB). In addition to resolution, the extreme sensitivity of rheology also offers modest protection from the imperfection of these forward models (Figure 4). Analytical rheology also offers other important advantages over other analytical techniques. It is easier and cheaper to perform, more sensitive to precisely those components that have the greatest relevance to processing, and circumvents the dissolution step, which offers its own set of challenges.
In closing, it is useful to emphasize once again what analytical rheology can do well and what it cannot. Rheology is a very sensitive probe of certain features of polymer architecture like molecular weight and LCB. These features are extremely significant for many commercially important synthetic polymers (primarily polyolefins) and that is the niche that analytical rheology occupies. But the potential heterogeneities, even while confining ourselves to synthetic polymers, extend far beyond that. Consider the example of poly(vinyl butyral)  which is used as an interlayer in laminated safety glass. It shows polydispersity in molar mass, chemical composition (it is a copolymer), SCB, and LCB. Sometimes it also exhibits crosslinking and graft-induced branching. In addition, the presence of intra- and intermolecular hydrogen bonding compounds dissolution, and, unlike well-studied polymers such as polyethylene, it lacks well-characterized narrow molecular weight linear standards. Clearly, even with perfect models and techniques for direct and inverse rheology, one cannot imagine fully characterizing such a polymer, using rheological techniques alone.
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The rheological behaviour of most polymeric materials is quite complex. The viscosity is both shear and thermal history dependent. Often, the polymer viscosity is measured off-line. A sample of polymer compound is melted and put into a special capillary tube (glass viscometer) or by incorporating a capillary tube mounted parallel to the extruder in case of online measurements. Both techniques involve long time delays resulting from the time required for the melt to flow through the transit lines and the capillary. In some cases, viscometers are mounted on the extrusion lines which measure the stress on the die wall by measuring the pressure drop along a slit or capillary and the flow rate is measured by an extra flow meter. Although these methods produce viscosity measurements more relevant to the extrusion process, the flow meter often disturbs the melt stream thus altering the original flow characteristics.
Our polymer science experts perform rheological property testing on a wide range of polymers such as polyolefins, liquids, adhesives, gels and pastes using a wide range of temperatures and deformation rates (both shear and extensional). Rheology tests are performed while the polymer is in the melt phase or while the polymer has been dissolved in a solvent for intrinsic viscosity and relative viscosity.
We can apply our rheology test capabilities in diagnostics, design or optimisation problems, using quantitative polymer rheology measurements to help you to optimise processing with minimal product degradation, or to optimise molding parameters which can lead to greater cost efficiencies costs and enhanced production rates.
Working across diverse industries such as automotive, aerospace, medical devices, industrial production and stakeholders in the polymer supply chain we deliver a detailed understanding of rheological properties through laboratory testing, helping you to optimize products and process conditions.
Dr. Edward B. Bagley was born in Alberta, Canada in 1927. He received a B.S. in both Chemistry and Physics with a Gold Medal for exemplary scholarship from the University of Western Ontario in 1950. He then obtained his Ph.D. in Physical Chemistry from Cornell University in 1954. After graduating from Cornell, Bagley worked at Canadian Industries Limited for ten years researching topics such as the melt rheology of high-density polyethylene. In 1964 he moved to an academic post to serve as Professor of Chemical Engineering at Washington University. In 1971 he returned to a research scientist position, this time at the Northern Regional Research Center of the United States Department of Agriculture (USDA). He was promoted to the position of Laboratory Chief at the USDA Engineering & Development Laboratory in Peoria in 1975 and stayed there until his retirement in 1995. 2b1af7f3a8