Viscoelastic polymer

The class of non-Newtonian fluids discussed above (i.e. fluids showing a shear-dependent viscosity) is simply one subset of the types of behaviour observed in polymeric fluids. The shear-dependent fluids considered above are assumed to be inelastic, although some polymer solutions show some degree of elasticity. When elastic materials are deformed through a small displacement they tend to return to their original configuration. If a shear stress is applied to an ideal solid, then for small displacements the displacement, which is the strain, y, is proportional to the applied stress and Hooke s 

Note that the simple Hooke s law behaviour of the stress in a solid is analogous to Newton s law for the stress of a fluid. For a simple Newtonian fluid the shear stress is proportional to the rate of strain, 7, (shear rate), whereas in a Hookian solid it is proportional to the strain, 7, itself. For a fluid which shares both viscous and elastic behaviour, the equation for the shear stress must incorporate both of these laws—Newton s and Hooke s. It was Maxwell who first realised that a possible constitutive relationship between the stress in a fluid and the strain is as follows  

Hookian solid. Note that in the above equation yy/G is a time constant, which we denote and we may write the equation for the stress, r(t), as follows (Bird et al, 1987a)  

The simple Maxwell model is not suitable for quantitative calculations on real viscoelastic fluids. However, it serves as a simple illustration of a 

Suppose a small amplitude oscillatory strain, y(t), is imposed on a fluid as follows  

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As mentioned earlier, the contact-mechanics-based experimental studies of interfacial adhesion primarily include (1) direct measurements of surface and interfacial energies of polymers and self-assembled monolayers (2) quantitative studies on the role of interfacial coupling agents in the adhesion of elastomers (3) adhesion of microparticles on surfaces and (4) adhesion of viscoelastic polymer particles. In these studies, a variety of experimental tools have been employed by different researchers. Each one of these tools offers certain advantages over the others. These experimental studies are reviewed in Section 4. 

Some of the recent work in contact mechanics is focused on understanding the adhesion of viscoelastic polymers and dynamic contributions to the adhesion energy this work is summarized in Section 5. Sections 6.1 and 6.2 include some of the current applications of contact mechanics in the field of adhesion science. These include possible studies on contact induced interfacial rearrangements and acid-base type of interactions. 

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. 

There are two further related sets of tests that can be used to give information on the mechanical properties of viscoelastic polymers, namely creep and stress relaxation. In a creep test, a constant load is applied to the specimen and the elongation is measured as a function of time. In a stress relaxation test, the specimen is strained quickly to a fixed amount and the stress needed to maintain this strain is also measured as a function of time. 

Polymers which creep readily have large values of / polymers which hardly creep at all have small values. For viscoelastic polymers below their glass transition temperature, there is a characteristic creep curve, as illustrated in Figure 7.6. 

Figure 7.6 Typical creep curve for a viscoelastic polymer...

Stress relaxation tests are alternative ways of measuring the same basic phenomenon in viscoelastic polymers as creep tests, Le. the time-dependent nature of their response to an applied stress. As such, they have also been of value in understanding the behaviour of these materials. The essence of stress relaxation tests is that strain increases with time for a given stress, so that if stress is decreased with time in a controlled manner ( relaxed ), a state... 

This second group of tests is designed to measure the mechanical response of a substance to applied vibrational loads or strains. Both temperature and frequency can be varied, and thus contribute to the information that these tests can provide. There are a number of such tests, of which the major ones are probably the torsion pendulum and dynamic mechanical thermal analysis (DMTA). The underlying principles of these dynamic tests have been covered earlier. Such tests are used as relatively rapid methods of characterisation and evaluation of viscoelastic polymers, including the measurement of T, the study of the curing characteristics of thermosets, and the study of polymer blends and their compatibility. They can be used in essentially non-destructive modes and, unlike the majority of measurements made in non-dynamic tests, they yield data on continuous properties of polymeric materials, rather than discontinuous ones, as are any of the types of strength which are measured routinely. 

For inelastic fluids exhibiting power-law behaviour, the bed expansion which occurs as the velocity is increased above the minimum fluidising velocity follows a similar pattern to that obtained with a Newtonian liquid, with the exponent in equation 6.31 differing by no more than about 10 per cent. There is some evidence, however, that with viscoelastic polymer solutions the exponent may be considerably higher. Reference may be made to work by Srimvas and Chhabra(15) for further details. 

Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

Research Focus Method of preparing viscoelastic polymers using crosslinked polyrotaxane inclusion complexes consisting of polyethylene glycol (PEG)-carboxyhc acid and a-cyclodextrin. 

Besides kinetic applications, which are still to be fully realized, hydro-dynamic modulation is useful for Schmidt number and diffusion coefficient measurements not only in Newtonian fluids but also in viscoelastic polymer solutions (Ostwald fluids) [291]. 

Fibrin is a viscoelastic polymer, which means that it has both elastic and viscous properties (Ferry, 1988). Thus, the properties of fibrin may be characterized by stiffness or storage modulus (representing its elastic properties) and creep compliance or loss modulus/loss tangent (representing its inelastic properties). These parameters will determine how the clot responds to the forces applied to it in flowing blood. For example, a stiff clot will not deform as much as a less stiff one with applied stress. 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

S. K. Goyal, E. Chu, and M. R. Kamal, Non-isothermal Radial Filling of Center-gated Disc Cavities with Viscoelastic Polymer Melts, J. Non-Newt. Fluid Meek, 28, 373-406 (1988). 

A. I. Leonov, Nonequilibrium Thermodynamics and rheology of viscoelastic polymer media, Rheol. Acta, 15, 85-98 (1976). 

Leonov AI (1976) Non-equilibrium thermodynamics and rheology of viscoelastic polymer medium. Reol Acta 15(2) 85-98... 

Pyshnograi GV (1996) An initial approximation in the theory of viscoelasticity of linear polymers and non-linear effects. J Appl Mech Techn Phys 37(1) 123—128 Pyshnograi GV (1997) The structure approach in the theory of flow of solutions and melts of linear polymers. J Appl Mech Techn Phys 38(3) 122—130 Pyshnograi GV, Pokrovskii VN (1988) Stress dependence of stationary shear viscosity of linear polymers in the molecular field theory. Polym Sci USSR 30 2624—2629 Pyshnograi GV, Pokrovskii VN, Yanovsky YuG, Karnet YuN, Obraztsov IF (1994) Constitutive equation on non-linear viscoelastic (polymer) media in zeroth approximation by parameter of molecular theory and conclusions for shear and extension. Phys — Doklady 39(12) 889-892... 

In sufficiently mobile, (i.e., liquid-like), systems, the anisotropy is averaged out by the isotropic thermal motions leaving only the isotropic contributions. As already stated, viscoelastic polymers represent an intermediate between the two extremes of rigid or mobile materials and the implications of this will be discussed in 14.2.3 in more detail. 

Figure 14.2 Scheme of a two-step decay of the correlation function S of a unit undergoing anisotropic motion before finally full isotropisation is achieved. The dashed line indicates the case of a one-step decay by isotropic motion. For the study of viscoelastic polymers the intermediate plateau that reflects residual couplings is the... 

For the investigation of the molecular dynamics in polymers, deuteron solid-state nuclear magnetic resonance (2D-NMR) spectroscopy has been shown to be a powerful method [1]. In the field of viscoelastic polymers, segmental dynamics of poly(urethanes) has been studied intensively by 2D-NMR [78, 79]. In addition to ID NMR spectroscopy, 2D NMR exchange spectroscopy was used to extend the time scale of molecular dynamics up to the order of milliseconds or even seconds. In combination with line-shape simulation, this technique allows one to obtain correlation times and correlation-time distributions of the molecular mobility as well as detailed information about the geometry of the motional process [1]. 

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