Linear dynamic viscoelastic properties

Temperature-Independent Correlations for the Linear Dynamic Viscoelastic Properties of Linear Flexible Homopolymers... 

Graessley and Stmglinski (1986) developed a theory, that predicts the linear dynamic viscoelastic properties of binary blends of monodisperse flexible homopolymers, based on the tube model, by incorporating constraint release and path fluctuations into the reptation motion (see Chapter 4). They assumed that the stress relaxation modulus of a binary blend, Gb(0, may be represented by... 

Here, we consider the rheological behavior of PS/PaMS blends exhibiting UCST. The miscibility and phase behavior of PS/PaMS blends have been studied (Cowies and McEwen 1985 Lau et al. 1982 Lin and Roe 1987, 1988 Rameau et al. 1989 Saeki et al. 1983 Schneider andDilger 1989 Wimpier and Maynard 1987) and the miscibility window of PS/PaMS blends has been found to be very sensitive to the molecular weights of the constituent components. We next consider the phase behavior and linear dynamic viscoelastic properties of three pairs of PS/PaMS blends, each having different molecular weights, as summarized in Table 7.1. 

PMMA/PSAN blends at temperatures below LCST. Here, we present the linear dynamic viscoelastic properties of PMMA/PSAN blends and compare them with theoretical predictions from the molecular theory presented in the preceding section. 

Lee and Han (2003b) investigated linear dynamic viscoelastic properties of organoclay nanocomposites based on both SI diblock copolymer and SIOH diblock copolymer. An SIOH diblock copolymer (referred to as SI-14/3-OH) was obtained by hydroxylation of the polyisoprene (PI) block of a highly asymmetric SI diblock copolymer (SI-14/3, with Af = 1.7 x 10" and = 1.08). SI-14/3 was a... 

Lee KM, Han CD (2003) Linear dynamic viscoelastic properties of functionalized block copolymer/organoclay nanocomposites. Mactomolecules 36 804-815... 

The dynamic viscoelastic properties of polymers are measured as a function of frequency or temperature. In the 1950s, a standard sample of polyisobutylene was distributed by the National Bureau of Standards, which requested that viscoelastic measurements, including stress relaxation, creep, forced vibration, and free vibration, be carried out by a number of cooperating laboratories. The data obtained from that study were compared and studied carefully, and the results contributed to the development of the science of linear viscoelastic properties of polymers [4,9]. 

From the dynamic viscoelastic properties, valuable information about the compatibility and phase separation of polymer blends [86-91] can be obtained, based on their sensitivity to variations in the morphology of blends. Some emulsion models for polymer blends [92-97] have been used to estimate the interfacial tension of HDPE/PS (80/20) blends. Chen et al. [98] used the linear rheological properties of... 

In this section, we present the molecular theory for the linear dynamic viscoelasticity of miscible polymer blends by Han and Kim (1989a, 1989b), which is based on the concept of the tube model presented in Chapter 4. Specifically, the reptation of two primitive chains of dissimilar chemical structures under an external potential will be considered, and the expressions for the linear viscoelastic properties of miscible polymer blends will be presented. We will first present the expressions for zero-shear viscosity ob. dynamic storage and loss moduli G co) and G " co), and steady-state compliance J° for binary miscible blends of monodisperse, entangled flexible homopolymers and then consider the effect of polydispersity. There are a few other molecular theories reported... 

Viscoelasticity of metal This subject provides an introduction on the viscoelasticity of metals that has no bearing or relationship with viscoelastic properties of plastic materials. The aim is to have the reader recognize that the complex thermodynamic foundations of the theory of viscoplasticity exist with metals. There have been developments in the thermodynamic approach to combined treatment of rheologic and plastic phenomena and to construct a thermodynamic theory non-linear viscoplastic material that may be used to describe the behavior of metals under dynamic loads. 

The mechanical response of polypropylene foam was studied over a wide range of strain rates and the linear and non-linear viscoelastic behaviour was analysed. The material was tested in creep and dynamic mechanical experiments and a correlation between strain rate effects and viscoelastic properties of the foam was obtained using viscoelasticity theory and separating strain and time effects. A scheme for the prediction of the stress-strain curve at any strain rate was developed in which a strain rate-dependent scaling factor was introduced. An energy absorption diagram was constructed. 14 refs. 

The viscoelastic response of polymer melts, that is, Eq. 3.1-19 or 3.1-20, become nonlinear beyond a level of strain y0, specific to their macromolecular structure and the temperature used. Beyond this strain limit of linear viscoelastic response, if, if, and rj become functions of the applied strain. In other words, although the applied deformations are cyclic, large amplitudes take the macromolecular, coiled, and entangled structure far away from equilibrium. In the linear viscoelastic range, on the other hand, the frequency (and temperature) dependence of if, rf, and rj is indicative of the specific macromolecular structure, responding to only small perturbations away from equilibrium. Thus, these dynamic rheological properties, as well as the commonly used dynamic moduli... 

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... 

Linear viscoelastic properties can be measured in two ways by static methods or by dynamic methods (Barnes et al., 1989). 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

The derivation of fundamental linear viscoelastic properties from experimental data obtained in static and dynamic tests, and the relationships between these properties, are described by Barnes etal. (1989), Gunasekaran and Ak (2002) and Rao (1992). In the linear viscoelastic region, the moduli and viscosity coefficients from creep, stress relaxation and dynamic tests are interconvertible mathematically, and independent of the imposed stress or strain (Harnett, 1989). 

When a sinusoidal strain is imposed on a linear viscoelastic material, e.g., unfilled rubbers, a sinusoidal stress response will result and the dynamic mechanical properties depend only upon temperature and frequency, independent of the type of deformation (constant strain, constant stress, or constant energy). However, the situation changes in the case of filled rubbers. In the following, we mainly discuss carbon black filled rubbers because carbon black is the most widespread filler in rubber products, as for example, automotive tires and vibration mounts. The presence of carbon black filler introduces, in addition, a dependence of the dynamic mechanical properties upon dynamic strain amplitude. This is the reason why carbon black filled rubbers are considered as nonlinear viscoelastic materials. The term non-linear viscoelasticity will be discussed later in more detail. 

The linear viscoelastic properties of all samples were characterized by dynamic shear measurements in the parallel-plate geometry. Experimental details have been previously published [9]. Using time-temperature equivalence, master curves for the storage and loss moduli were obtained. Fig. 1 shows the master curves at 140°C for the relaxation spectra and Table 3 gives the values of zero-shear viscosities, steady-state compliances and weight-average relaxation times at the same temperature. 

---