Viscoelasticity polymer fundamentals

Viscoelastic polymers essentially dominate the multi-billion dollar adhesives market, therefore an understanding of their adhesion behavior is very important. Adhesion of these materials involves quite a few chemical and physical phenomena. As with elastic materials, the chemical interactions and affinities in the interface provide the fundamental link for transmission of stress between the contacting bodies. This intrinsic resistance to detachment is usually augmented several folds by dissipation processes available to the viscoelastic media. The dissipation processes can have either a thermodynamic origin such as recoiling of the stretched polymeric chains upon detachment, or a dynamic and rate-sensitive nature as in chain pull-out, chain disentanglement and deformation-related rheological losses in the bulk of materials and in the vicinity of interface. 

In a fundamental sense, the miscibility, adhesion, interfacial energies, and morphology developed are all thermodynamically interrelated in a complex way to the interaction forces between the polymers. Miscibility of a polymer blend containing two polymers depends on the mutual solubility of the polymeric components. The blend is termed compatible when the solubility parameter of the two components are close to each other and show a single-phase transition temperature. However, most polymer pairs tend to be immiscible due to differences in their viscoelastic properties, surface-tensions, and intermolecular interactions. According to the terminology, the polymer pairs are incompatible and show separate glass transitions. For many purposes, miscibility in polymer blends is neither required nor de-... 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

Northolt MG, Kampschreur JH, Van derZwaagS (1989) Viscoelasticity of aramid fibres. In Lemstra PJ.Kleintjes LA (eds) Integration of fundamental polymer science and technology. Elsevier, London, p 157... 

The purpose of this paper is to establish the fundamental links between the glass transition, viscoelastic relaxation, and yield stress by investigating the relaxation processes in polymers. The relationship between temperature and relaxation time scale is represented by a shift factor (a). At temperature T... 

Thus, fundamentally the interest is in testing the limits and theory of polymer behavior in end-tethered systems, e.g., viscoelastic behavior, wetting and surface energies, adhesion, shear forces relevant to tribology, etc. It should be noted that relevant surfaces and interfaces can also refer to polymers adsorbed in liquid-liquid, liquid-gas, solid-gas, and solid-liquid interfaces, which makes these polymer systems also of prime importance in interfacial science and colloidal phenomena (Fig. 2). Correspondingly, a wide number of potential applications can be enumerated ranging from lubrication and microelectronics to bioimplant surfaces. 

Despite the similarities in brittle and ductile behavior to ceramics and metals, respectively, the elastic and permanent deformation mechanisms in polymers are quite different, owing to the difference in structure and size scale of the entities undergoing movement. Whereas plastic deformation (or lack thereof) could be described in terms of dislocations and slip planes in metals and ceramics, the polymer chains that must be deformed are of a much larger size scale. Before discussing polymer mechanical properties in this context, however, we must first describe a phenomenon that is somewhat unique to polymers—one that imparts some astounding properties to these materials. That property is viscoelasticity, and it can be described in terms of fundamental processes that we have already introduced. 

As already stated, mastication reactions are not limited to elastomers but can be extended to all polymers in the viscoelastic state. It is thus interesting to note that before the fundamental study of Watson and coworkers on cold rubber... 

When the experimentalist set an ambitious objective to evaluate micromechanical properties quantitatively, he will predictably encounter a few fundamental problems. At first, the continuum description which is usually used in contact mechanics might be not applicable for contact areas as small as 1 -10 nm [116,117]. Secondly, since most of the polymers demonstrate a combination of elastic and viscous behaviour, an appropriate model is required to derive the contact area and the stress field upon indentation a viscoelastic and adhesive sample [116,120]. In this case, the duration of the contact and the scanning rate are not unimportant parameters. Moreover, bending of the cantilever results in a complicated motion of the tip including compression, shear and friction effects [131,132]. Third, plastic or inelastic deformation has to be taken into account in data interpretation. Concerning experimental conditions, the most important is to perform a set of calibrations procedures which includes the (x,y,z) calibration of the piezoelectric transducers, the determination of the spring constants of the cantilever, and the evaluation of the tip shape. The experimentalist has to eliminate surface contamination s and be certain about the chemical composition of the tip and the sample. 

J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1971 also, S. Middleman, Fundamentals of Polymer Processing, McGraw-Hill, New York, 1977, p. 472. 

Investigation of viscoelastic behaviour of linear polymer solutions and melts shows that there are universal laws for dependencies of the terminal characteristics on the length of macromolecules, which allows to interpret these phenomena on the base of behaviour of a single macromolecule in the system of entangled macromolecules (Ferry 1980, Doi and Edwards 1986). The validity of the mesoscopic approach itself rests essentially on the fundamental experimental fact that quantities that characterise the behaviour of a polymer system have a well-defined unambiguous dependence on the length of the macromolecule. 

From a more fundamental point of view, the selection of different inden-ter geometries and loading conditions offer the possibility of exploring the viscoelastic/viscoplastic response and brittle failure mechanisms over a wide range of strain and strain rates. The relationship between imposed contact strain and indenter geometry has been quite well established for normal indentation. In the case of a conical or pyramidal indenter, the mean contact strain is usually considered to depend on the contact slope, 0 (Fig. 2a). For metals, Tabor [32] has established that the mean strain is about 0.2 tanG, i.e. independent of the indentation depth. A similar relationship seems to hold for polymers although there is some indication that the proportionality could be lower than 0.2 for viscoelastic materials [33,34], In the case of a sphere, an... 

In discussing shear deformation, it is convenient to distinguish between the initial elastic and viscoelastic response of the polymer to the applied load and the subsequent time-dependent response. However, the distinction is somewhat arbitrary and is not as fundamental as that between elastic volume response and crazing. Viscoelastic shear deformation continues throughout the period under load. The observed time-dependence of lateral strain reflects both generalized viscoelastic relaxation and shear band formation. Since crazing consists simply of displacement in the tensile stress direction, it makes no contribution to lateral strain therefore —e specifically measures deformation by shear processes. 

The resonant beam test technique forms the basis of the ASTM Standard E756-83 for measuring the viscoelastic properties of damping materials. Fundamentally, the beam test requires that the resonant frequencies of a metal-beam, mounted in cantilever fashion, be determined as a function of temperature and frequency the beam is then coated with a polymer and the resonant frequencies and corresponding modal damping of the composite beam are determined as a function of temperature and frequency. From these two data sets, the vibration damping properties of the polymer can be evaluated. The ASTM Standard provides the necessary equations to obtain the complex modulus data from the collected test data and also provides guidelines for the proper choice of the specimens (1.21. The principal difference between the beam test and the other methods used here is that the beam test calculates the material properties from the test results on the metal beam and the composite beam whereas the... 

The stress in viscoelastic liquids at steady-state conditions is defined, in simple shear flow, by the shear rate and two normal stress differences. Chapter 13 reviews the evolution of both the normal stress differences and the viscosity with increasing shear rate for different geometries. Semiquantitative approaches are used in which the critical shear rate at which the viscosity starts to drop in non-Newtonian fluids is estimated. The effects of shear rate, concentration, and temperature on die swell are qualitatively analyzed, and some basic aspects of the elongational flow are discussed. This process is useful to understand, at least qualitatively, the rheological fundamentals of polymer processing. 

The relaxation time r is a fundamental dynamic property of all viscoelastic liquids. Polymer liquids have multiple relaxation modes, each with its own relaxation time. Any stress relaxation modulus can be described by a series combination of Maxwell elements. 

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