Polymer rheology viscoelasticity

Contents Chain Configuration in Amorphous Polymer Systems. Material Properties of Viscoelastic Liquids. Molecular Models in Polymer Rheology. Experimental Results on Linear Viscoelastic Behavior. Molecular Entan-lement Theories of Linear iscoelastic Behavior. Entanglement in Cross-linked Systems. Non-linear Viscoelastic-Properties. 

Polymers are viscoelastic materials meaning they can act as liquids, the visco portion, and as solids, the elastic portion. Descriptions of the viscoelastic properties of materials generally falls within the area called rheology. Determination of the viscoelastic behavior of materials generally occurs through stress-strain and related measurements. Whether a material behaves as a viscous or elastic material depends on temperature, the particular polymer and its prior treatment, polymer structure, and the particular measurement or conditions applied to the material. The particular property demonstrated by a material under given conditions allows polymers to act as solid or viscous liquids, as plastics, elastomers, or fibers, etc. This chapter deals with the viscoelastic properties of polymers. 

Rheology is the study of deformation and flow of materials. Polymers are viscoelastic materials, meaning they can act as liquids and as solids. 

Natural and biomedical polymers Organometallic polymers Inorganic polymers Reactions of polymers Rheology (flow properties, viscoelasticity)... 

This section contains two primary topics. The first is polymer rheology, which is concerned with how polymeric materials flow when they are placed under stress. Also of interest are the mechanical properties of polymers, particularly their elasticity. The combination of viscous effects with elastic phenomena is called viscoelasticity. 

Fatkullin NF, Kimmich R, Kroutieva M (2000) The twice-renormalised Rouse formalism of polymer dynamics Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation. J Exp Theor Phys 91(1) 150-166 Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, London Ferry JD (1990) Some reflections on the early development of polymer dynamics Viscoelasticity, dielectric dispersion, and self-diffusion. Macromolecules 24 5237-5245 Ferry JD, Landel RF, Williams ML (1955) Extensions of the Rouse theory of viscoelastic properties to undilute linear polymers. J Appl Phys 26 359-362 Fikhman VD, Radushkevich BV, Vinogradov GV (1970) Reological properties of polymers under extension at constant deformation rate and at constant extension rate. In Vinogradov GV (ed) Uspekhi reologii polimerov (Advances in polymer rheology, in Russian). Khimija, Moscow, pp 9-23... 

It is well known in polymer rheology that a torsional parallel-plate flow cell develops certain secondary flow and meniscus distortion beyond some stress level [ 14]. For viscoelastic melts, this can happen at an embarrassingly low stress. The critical condition for these instabilities has not been clearly identified in terms of the shear stress, normal stress, and surface tension. It is very plausible that the boundary discontinuity and stress intensification discussed in Sect. 4 is the primary source for the meniscus instability. On the other hand, it is well documented that the first indication of an unstable flow in parallel plates is not a visually observable meniscus distortion or edge fracture, but a measurable decay of stress at a given shear rate [40]. The decay of the average stress can occur in both steady shear and frequency-dependent dynamic shear. 

In standard polymer rheology, there are no inertial effects and is always negative [72]. The choice of the exponents and does affect the derived values of the compliance. Generally speaking, viscoelastic dispersion applies to all viscoelastic parameters, not just the compliance of the film. However, for the crystal and the electrodes, the viscoelastic dispersion is often weaker than for polymer films. 

As has already been stated, the verified possibility of extending the reduced variables principles to ABS resins makes it possible to treat these typical heterophase systems as blends of amorphous homophase polymers and plasticizers. One possible explanation is that over the experimental y range it is not possible to separate the contributions of the two different phases, and the materials will behave as homophase polymer. In fact, long-time molten polymer rheology experiments measure viscoelastic processes over the entire molecule, and, as a consequence, molecular compatibility is evaluated (13). On the other hand, high frequency and/or low temperature tests involve the main chain as well as the side chains of the polymer system the segmental miscibility of the polymer-polymer system is then evaluated. It is important in experimental measurements of polymer compatibility to evaluate the actual size of the volume subject to the test. 

It should be noted here that in polymer rheology, for viscoelastic fluids the commonly used dimensionless parameter to characterize the ratio of elastic force to viscous force is the Deborah number denoted by the symbol De. This parameter is essentially just the Peclet number. In terms of characteristic times, it is equal to the ratio of the largest time constant of the molecular motions or other appropriate relaxation time of the fluid compared to the characteristic flow time. 

Accessible precursor architectures (building imits, dimensionality of the polymer molecule) are dictated by the methods of the chemical synthesis of the monomer units and the associated polymerization reactions. The type of shape-forming procedure used (fiber-extrusion firom solution or melt, spincoating, etc.) engenders constraints on what is considered useful polymer rheology. Especially in the case of fiber-drawing or -extrusion the precursor should exhibit thixotropic or non-Newtonian viscoelastic behavior. The viscosity should be sufficiently high at zero shear such that once formed, the material will retain its new shape. 

For the polymers derived by polymerization with methylamine from TADB, MADE, and DADB, respectively, rheological studies have been performed. While the TADB-based polymer exhibits viscoelastic behavior, with the viscous contribution being 10 times higher than the elastic one, the MADB-and DADB-based polymers show an almost purely viscous behavior. For the latter two polymers, the ratio of the viscous and the elastic contributions amounts to 100. Furthermore, it has been foimd that the TADB-based polymer shows a higher tendency to further crosslinking than the MADE- and DADB-based polymers [93]. 

In the last chapter we discussed the relation between stress and strain (or instead rate-of-strain) in one dimension by treating the viscoelastic quantities as scalars. When the applied strain or rate-of-strain is large, the nonlinear response of the polymeric liquid involves more than one dimension. In addition, a rheological process always involves a three-dimensional deformation. In this chapter, we discuss how to express stress and strain in three-dimensional space. This is not only important in the study of polymer rheological properties in terms of continuum mechanics " but is also essential in the polymer viscoelastic theories and simulations studied in the later chapters, into which the chain dynamic models are incorporated. 

Polymers are viscoelastic in nature. They have interesting rheological properties, which exhibit elasticity and viscous flow [1]. During the application of stress, the polymeric material undergoes a strain, which is dependent upon the applied stress. Removal of stress on the material may not return to its original dimensions, which has certain permanent... 

The presence of a confined interfacial layer, with specific rheological behavior, is proposed to explain this complex behavior. The low stiffness of PDMS allows a competition between the (low) cohesion and the confined chain layer at the PDMS surface and the adhesion level (interfacial interactions between PDMS and substrates). At low speeds, interfacial interactions have a significant effect and partly govern the friction, and at high speeds the influence of the substrate surface becomes negligible and friction is then governed by the polymer s intrinsic viscoelastic behavior. Experimental results underline the subtle competition between interfacial interactions and polymer rheological properties, especially for PDMS samples. Comparison... 

Yanovski Yu G, Vinogradov G V, Ivanova L N (1982) Viscoelasticity of blends of narrow molecular mass distribution polymers. In Novyje aspecty v reologii poli-merov (New Items in Polymer Rheology, in Russian) part 1. INKHS AN USSR, Moscow, p 80... 

Polymers are viscoelastic materials, whose mechanical behavior exhibits characteristics of both solids and liquids. Thermal analysts are frequently called on to measure the mechanical properties of polymers for a number of purposes. Of the different methods for viscoelastic property characterization, dynamic mechanical techniques are the most popular, since they are readily adapted for studies of both polymeric solids and liquids. They are often referred to collectively as dynamic mechanical analysis (DMA). Thermal analysts often refer to the DMA measurements on liquids as rheology measurements. 

In polymer rheology, and are important because at these points drastic change occurs in the hydrodynamic nature of the states, that is, glassy, viscoelastic, and viscous fluid. Transitions can be dealt with using thermodynamics and kinetics. 

Filled polymer rheology is basically concerned with the description of the deformation of filled polymer systems under the influence of applied stresses. Softened or molten filled polymers are viscoelastic materials in the sense that their response to deformation lies in varying extent between that of viscous liquids and elastic solids. In purely viscous liquids, the mechanical energy is dissipated into the systems in the form of heat and cannot be recovered by releasing the stresses. Ideal solids, on the other hand, deform elastically such fliat the deformation is reversible and the energy of deformation is fully recoverable when the stresses are released. 

The book begins with introductory material and a brief review of fundamentals, after which the first part focuses on analytical treatments of basic polymer processes extrusion, mold filling, fiber spinning, and so forth. The thin gap (lubrication) and thin filament approximations are employed, and all analyses in this part are for inelastic liquids. An introduction to finite element calculation follows, where full numerical solutions are compared to analytical results. Polymer rheology is then introduced, with an emphasis on relatively simple viscoelastic models that have been used with some success to model processing operations. Applications in which melt viscoelasticity is important are then revisited, followed by a chapter on stability and sensitivity that focuses on melt spinning and a chapter on wall slip and extrusion... 

The results of a number of studies on polymer rheology in porous media are then reviewed. Firstly, results for pseudoplastic fluids (mainly xanthan) are discussed and then results are reviewed for fluids showing some viscoelastic/extensional viscosity behaviour (e.g. HPAM, PEO). In all of these studies, flow is purely single-phase, and most experiments have been performed at 100% water saturation in the porous pack or core, although a few have been done at residual oil. 

Molten polymers are viscoelastic materials, and so study of their behaviour can be complex. Polymers are also non-ideal in behaviour, i.e. they do not follow the Newtonian liquid relationship of simple liquids like water, where shear-stress is proportional to shear strain rate. Unlike Newtonian liquids, polymers show viscosity changes with shear rate, mainly in a pseudoplastic manner. As shear rate increases there is a reduction in melt viscosity. This is true of both heat-softened plastics and rubbers. Other time-dependent effects will also arise with polymer compounds to complicate the rheological process behaviour. These may be viscosity reductions due to molecular-mass breakdown or physical effects due to thixotropic behaviour, or viscosity increases due to crosslinking/branching reactions or degradation. Generally these effects will be studied in rotational-type rheometers and the extrusion-type capillary rheometer. 

Because polymer rheology is a deeply complex field [62-64], there are many other methods to assess different types of viscoelastic and mechanical behavior of polymers in concentrated solutions, melts, and rubbery states. 

---