Bulk viscoelasticity

The premise of the above analysis is the fact that it has treated the interfacial and bulk viscoelasticity equally (linearly viscoelastic experiencing similar time scales of relaxation). Falsafi et al. make an assumption that the adhesion energy G is constant in the course of loading experiments and its value corresponds to the thermodynamic work of adhesion W. By incorporating the time-dependent part of K t) into the left-hand side (LHS) of Eq. 61 and convoluting it with the evolution of the cube of the contact radius in the entire course of the contact, one can generate a set of [LHS(t), P(0J data. By applying the same procedure described for the elastic case, now the set of [LHS(t), / (Ol points can be fitted to the Eq. 61 for the best values of A"(I) and W. 

The energy release rate (G) represents adherence and is attributed to a multiplicative combination of interfacial and bulk effects. The interface contributions to the overall adherence are captured by the adhesion energy (Go), which is assumed to be rate-independent and equal to the thermodynamic work of adhesion (IVa)-Additional dissipation occurring within the elastomer is contained in the bulk viscoelastic loss function 0, which is dependent on the crack growth velocity (v) and on temperature (T). The function 0 is therefore substrate surface independent, but test geometry dependent. 

An investigation of the mechanism of adhesive failure of polydimethylsiloxane elastomers was conducted [75]. The study showed that the total adhesive failure energy could be decomposed into energies for breaking chemical bonds, breaking physical bonds and deforming the bulk viscoelastic elastomer. 

In contrast, in the case of the contact deformation displacement of ball-to-flat counterformal contacts discussed above no effect of adhesion was found as compared with the influence of the (bulk) viscoelastic properties of the materials. (This may be due to elastic relief forces which may burst adhesive junctions during the loadingunloading contact deformation cycles.)... 

Figure 6 shows the master curves for the PS films with M of 4.9k and 140k drawn by horizontal and vertical shifts of each curve shown in Fig. 5 at the reference temperatures of 267 and 333 K, respectively [26]. The master curves obtained from the dependence of lateral force on the scanning rate were very similar to the lateral force-temperature curves, as shown in Fig. 3. Hence, it seems plausible as a general concept that the scanning rate dependence of the lateral force exhibits a peak in a glass-rubber transition. Also, it is clear that the time-temperature superposition principle, which is characteristic of bulk viscoelastic materials [35], can be applied to the surface relaxation process as well. Assuming that Uj has a functional form of Arrhenius type [36, 37], the apparent activation energy for the aa-relaxati(Mi process, A//, is given by ...

Increasing polymer concentration affects chain scission in several ways, as it increases the bulk viscoelasticity, the stress transmission efficiency, tq, and the hydrodynamic screening. The hydrodynamic screening means the hydrodynamic interactions become negligible between chain segments whose spatial distance apart is larger than a certain value (termed hydrodynamic screen length). In both... 

Study of the bulk viscoelastic properties of 11a are hampered by the crystallinity of the material, even though crystallization is slow. By introducing linkers with a mixed methyl substitution pattern, noncrystallizing supramolecular polymer 11b was obtained, which was studied using dynamic mechanical thermal analysis (DMTA), rheology, and dielectric relaxation spectroscopy [20]. 

The surface forces, of van der Waals type for rubber-like materials, are able to grandly modify the stress tensor provided by the contact of a blunt asperity applied against the flat and smooth surface of a rubber sample. It will be shown how the coupling of surface adhesion properties and bulk viscoelastic behavior of rubber-like material allows us to solve adherence problems. This will be illustrated through three examples the spontaneous peeling due to the intervention of internal stresses the no-rebound of balls on the smooth surfoce of a soft elastomer and the adhesive contact and rolling of a rigid cylinder under a smooth-surfaced sheet of rubber. 

When a driver jams on the brakes he thinks usually that the deceleration of the vehicle results from this action, but the true reason why the vehicle stops is in fact the great force induced by friction at the tire-road interface. It will be shown that this fiiction force is the direct result of the coupling of surface adhesion properties and bulk viscoelastic behavior of rubber-like materials. 

Figure 6. Rebound hdghts of six polished balls made of stainless steel, of diameters 2, 3,4, 6, 8 and 10 mm, dropped on the horizontal, plmie and smooth surface of a soft natural rubber sample (Young s modulus iM).89 MPa and Poisson s ratio v=0.5). Curves I. the s ace was cleai with pure ethanol and dried with air, so that sur ce effects, due to van der Waals forces, were superimposed on bulk viscoelastic propmies. Curve II the sur ce was dusted with talcum powder to prevent adhesion. Experimental data (symbols) correlate quite well mth computed predictions (heavy lines).

Figure 6. (a) Frictional force versus temperature for a PMMA film, (b) Frictional force versus temperature for a PET film, (c) Frictional force versus temperature for a PS film. Figures a-c overlaid with literature bulk viscoelastic data. 

It seems desirable at this point to familiarize the reader with some concrete examples of the viscoelastic phenomena defined in the preceding chapter, and to provide an idea of their character as exhibited by various types of polymeric systems. Linear viscoelastic behavior in shear will be illustrated in considerable detail, with a few additional examples of bulk viscoelastic behavior and nonlinear phenomena. The examples are accompanied by some qualitative remarks about molecular interpretation, anticipating Chapters 9 and 10 where molecular theories will be discussed more quantitatively. 

As an example of bulk viscoelastic behavior, data for a poly(vinyl acetate) of moderately high molecular weight are shown in Fig. 2-9. Measurements by McKinney and Belcher of the storage and loss bulk compliance B and B" at various temperatures and pressures are plotted after reduction to a reference temperature and pressure of 50°C and 1 atm respectively (see Chapter 11). The complex bulk compliance is formally analogous to the complex shear compliance, but the two functions present several marked contrasts. 

Viscoelastic behavior in simple extension or in bulk longitudinal deformation will in general combine the features of shear and bulk viscoelasticity, since the moduli E t) and M t) depend on both (7(0 and K t), as shown by equations 51 and 58 of Chapter 1 ( and analogous relations for E and M ). However, as already pointed out, shear effects predominate in E(t) and E. and bulk effects predominate... 

FIG.8-1. Diagram of method of McKinney, Edelman, and Marvin for measuring dynamic bulk viscoelastic properties. 

Values of dT/dP)r have been determined for a number of polymers " from bulk viscoelasticity measurements (Chapter 18) or dielectric or nuclear magnetic resonance measurements (Section E below). They are listed in Table 1 l-III. The magnitude of this derivative is generally 0.020 0.005 deg/atm. From equation 59 and the observation in Table 1 l-II that a/ is generally near 5 X lO" deg (within a factor of 2), it may be concluded that /3y is of the order of 1 X 10 atm or 1 X 10 " cm /dyne, though substantial differences from one polymer to another may be expected. 

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. 

Molecular motions very similar to some of these may also occur in vitrifying liquids of low molecular weight near and below Tg. Indeed, the bulk viscoelastic properties, as evidenced by the course of volume contraction near Tg illustrated in Fig. 11 -7 and discussed further in Chapter 18, seem to be very similar for both polymers and small molecules (Section B1 of Chapter 18). In shear viscoelastic properties, however, there are some characteristic differences, and it is instructive to examine the behavior of small molecules first. 

Transient experiments of bulk viscoelasticity are generally of interest only at temperatures below about Tg + 20°, since otherwise the volume changes are too rapid for convenient observation. At higher temperatures, the equilibrium bulk modulus Ke and thermodynamic compressibility j8 = have been determined for numerous polymers. ... 

The volume change following a sudden pressure change AP = P2 P can be described in the range of linear bulk viscoelastic behavior by the relation... 

In dynamic bulk viscoelastic measurements, the deformations are ordinarily exceedingly small and therefore in the linear range of behavior the change in free volume during a cycle of deformation is a very small proportion of the total free volume. However, a large constant hydrostatic pressure can be imposed if desired on the small periodic pressure changes, thereby altering the free volume and hence the relaxation times and the frequency scale of the viscoelastic dispersion. 

The conventional reduced curves plotted against reduced frequency are obtained by choosing cu as the independent variable in equation 6 and reducing B and B" to To and Pq by equations 8-11, then plotting against ojat-p where = a 12 is given in terms of free volume by equations 49 and 58 of Chapter 11. For this purpose, / was taken as 4.8 X 10-" deg , jS/ as 0.96 X 10- cm2/dyne, and/ = 0.025 at 17 C and 1 atm. The results have already been seen in Fig. 2-9 as the Classical example of bulk viscoelastic behavior. 

The Mooney viscosity is the torque generated on a spindle rotating at constant angular velocity, immersed in a polymeric material between heated dies. It is one of the most widely used industrial measures of bulk viscoelastic properties of polymeric materials, especially elastomers and rubbers. Oftentimes, the Mooney viscosity is of greater practical significance than the dynamic mechanical determination of G and G". The notion of Mooney viscosity is well grounded in the principles of continuum mechanics but involves the empirically determined Mooney viscosity and related parameters. 

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