Bulk Volume Viscoelasticity

The inclusion of values in Table 1 l-III derived from dynamic bulk viscoelastic measurements implies the concept that the relaxation times describing time-de-pendent volume changes also depend on the fractional free volume—consistent with the picture of the glass transition outlined in Section C. In fact, the measurements of dynamic storage and loss bulk compliance of poly(vinyl acetate) shown in Fig. 2-9 are reduced from data at different temperatures and pressures using shift factors calculated from free volume parameters obtained from shear measurements, so it may be concluded that the local molecular motions needed to accomplish volume collapse depend on the magnitude of the free volume in the same manner as the motions which accomplish shear displacements. Moreover, it was pointed out in connection with Fig. 11 -7 that the isothermal contraction following a quench to a temperature near or below Tg has a temperature dependence which can be described by reduced variables with shift factors ay identical with those for shear viscoelastic behavior. These features will be discussed more fully in Chapter 18. 

In steady-state shear flow at very low rates of shear 7, the primary normal stress difference c — 022 is related to the dynamic storage modulus at very low 

---

Measurements of physical properties usually encompass the whole, undisturbed sediment. Two types of parameters can be distinguished (1) bulk parameters and (2) acoustic and elastic parameters. Bulk parameters only depend on the relative amount of solid and fluid components within a defined sample volume. They can be approximated by a simple volume-oriented model (Fig. 2.2a). Examples are the wet bulk density and porosity. In contrast, acoustic and elastic parameters depend on the relative amount of solid and fluid components and on the sediment frame including arrangement, shape and grain size distribution of the solid particles. Viscoelastic wave propagation models simulate these complicated structures, take the elasticity of the frame into account and consider interactions between solid and fluid constituents. (Fig. 2.2b). Examples are the velocity and attenuation of P-and S-waves. Closely related parameters which mainly depend on the distribution and capillarity of the pore space are the permeability and electrical resistivity. 

Here, Ax denotes a difference between the viscoelastic terminal relaxation times of the component X (= PI, PtBS) in bulk, Xg,x " / and in the blend, Xg,x-Ix represents a difference of the entanglement plateau heights normalized to unit volume fraction of the component X in bulk and blend. Ix is determined according to the mixing rules. Equations (3.60) through (3.62). 

Housiadas and Tanner (2009), following the approach of Greco et al. (2005), have used a perturbation analysis to obtain the analytical solution for the pressure and the velocity field up to 0 (pDe) of a dilute suspension of rigid spheres in a weakly viscoelastic fluid, where

volume fraction of the spheres and De is the Deborah number of the viscoelastic fluid. The analytical solution was used to calculate the bulk first and second normal stress in simple shear flows and the elongational viscosity. The main results are... 

Molecular dynamics (MD) is an invaluable tool to study structural and dynamical details of polymer processes at the atomic or molecular level and to link these observations to experimentally accessible macroscopic properties of polymeric materials. For example, in their pioneering studies of MD simulations of polymers, Rigby and Roe in 1987 introduced detailed atomistic modeling of polymers and developed a fundamental understanding of the relationship between macroscopic mechanical properties and molecular dynamic events [183-186]. Over the past 15 years, molecular dynamics have been applied to a number of different polymers to study behavior and mechanical properties [187-193], polymer crystallization [194-196], diffusion of a small-molecule penetrant in an amorphous polymer [197-199], viscoelastic properties [200], blend [201,202] and polymer surface analysis[203-210]. In this article, we discuss MD studies on polyethylene (PE) with up to 120,000 atoms, polyethylproplyene (PEP), atactic polypropylene (aPP) and polyisobutylene (PIB) with up to 12,000 backbone atoms. The purpose of our work has been to interpret the structure and properties of a fine polymer particle stage distinguished from the bulk solid phase by the size and surface to volume ratio. 

Due to the fact that non-Fickean diffusion is influenced by a change in the free volume of the adhesive, the viscoelastic bulk and shear compliances in the form of two separate Prony series are used. Poisson s ratio is allowed to vary with time for the adhesive. A shift factor definition based on the free-volume concept is used in the analysis. The adhesive is assumed to be initially moisture-free. A moisture concentration value of unity is specified on the adhesive boundary. 

The applied signal can be either the pressure change at the opposite end of the capillary (Fig. 2) [16, 17] as in the previous case, or the volume variation in the cell produced by a pulsating rod or a piezodriver at constant pressure near the opposite capillary end (Fig. 3) [4, 14, 18-20]. In all cases from the comparison of the applied and the measured signals the complex dilational viscoelasticity c(i(o) can be obtained as a function of frequency after elimination of all contributions caused by the bulk phase behaviour. It is possible also to measure both the pressure in the cell and the meniscus volume and to compare them [21-23]. 

---