Viscoelastic behavior temperature dependence

In view of these complexities, it is remarkable that Eq. 4.1-4 represents numerous metal-metal, dry frictional data rather well, for both the static and sliding cases. Polymers, on the other hand, exhibit an even more complex frictional behavior on metal. This is, perhaps, not surprising, since the physical situation involves a relatively soft, viscoelastic, and temperature-dependent material in contact with a hard, elastic, and much less temperature- and rate-dependent material. Empirical evidence of these complexities is the nonlinear relationship between the frictional force and the normal load... 

For those not familiar with this type information recognize that the viscoelastic behavior of plastics shows that their deformations are dependent on such factors as the time under load and temperature conditions. Therefore, when structural (load bearing) plastic products are to be designed, it must be remembered that the standard equations that have been historically available for designing steel springs, beams, plates, cylinders, etc. have all been derived under the assumptions that (1) the strains are small, (2) the modulus is constant, (3) the strains are independent of the loading rate or history and are immediately reversible, (4) the material is isotropic, and (5) the material behaves in the same way in tension and compression. 

Viscoelasticity A combination of viscous and elastic properties in a plastic with the relative contribution of each being dependent on time, temperature, stress, and strain rate. It relates to the mechanical behavior of plastics in which there is a time and temperature dependent relationship between stress and strain. A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid. 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

The time and temperature dependent properties of crosslinked polymers including epoxy resins (1-3) and rubber networks (4-7) have been studied in the past. Crosslinking has a strong effect on the glass transition temperature (Tg), on viscoelastic response, and on plastic deformation. Although experimental observations and empirical expressions have been made and proposed, respectively, progress has been slow in understanding the nonequilibrium mechanisms responsible for the time dependent behavior. 

Polymers are viscoelastic materials meaning they can act as liquids, the visco portion, and as solids, the elastic portion. Descriptions of the viscoelastic properties of materials generally falls within the area called rheology. Determination of the viscoelastic behavior of materials generally occurs through stress-strain and related measurements. Whether a material behaves as a viscous or elastic material depends on temperature, the particular polymer and its prior treatment, polymer structure, and the particular measurement or conditions applied to the material. The particular property demonstrated by a material under given conditions allows polymers to act as solid or viscous liquids, as plastics, elastomers, or fibers, etc. This chapter deals with the viscoelastic properties of polymers. 

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

The viscoelastic samples to be tested by this method may be in different forms. The simplest to work with is a soft or liquid-like viscoelastic material such as mayonnaise or other food emulsions. These are easy samples to work with terms of sample loading. More solid-like samples such as cheese or food gels are more difficult to load onto the instrument in a consistent matter. The degree of compression of soft samples should ideally be controlled using a normal force measure or force rebalance system. Slippage is also a concern and roughened plates or even adhesives may be needed if slip is an issue. As this protocol is a general one, it is assumed that the sample is already loaded on the rheometer and has achieved equilibrium in terms of temperature and viscoelastic stmcture (time-dependent behavior). 

Thixotropy is the tendency of certain substances to flow under external stimuli (e.g., mild vibrations). A more general property is viscoelasticity, a time-dependent transition from elastic to viscous behavior, characterized by a relaxation time. When the transition is confined to small regions within the bulk of a solid, the substance is said to creep. A substance which creeps is one that stretches at a time-dependent rate when subjected to constant stress and temperature. The approximately constant stretching rates at intermediate times are used to characterize the creeping characteristics of the material. 

On the basis of our experimental results presented so far, the overall viscoelastic behavior of these triblock copolymers shows an elasticity-dominance over the viscosity. After reaching the critical mass density, where the static elasticity es reaches the maximum, these triblock copolymers collapse into the subphase and form hydrated brushes and these anchored brushes may be responsible for the result that the surface viscosities drop to around the 0 value at r. A distinctive difference between two types of polymers, sample I (PEO-PPO-PEO) and sample II (PPO-PEO-PPO), is the temperature dependence of r where both static elasticity and dilational viscosity show kinds of transitions. V of sample I increases with increasing temperature while that of sample II does not change with temperature. 

There are several analytical tools that provide methods of extrapolating test data. One of these tools is the Williams, Landel, Ferry (WLF) transformation.14 This method uses the principle that the work expended in deforming a flexible adhesive is a major component of the overall practical work of adhesion. The materials used as flexible adhesives are usually viscoelastic polymers. As such, the force of separation is highly dependent on their viscoelastic nature and is, therefore, rate- and temperature-dependent. Test data, taken as a function of rate and temperature, can be expressed in the form of master curves obtained by WLF transformation. This offers the possibility of studying adhesive behavior over a sufficient range of temperatures and rates for most practical applications. Fligh rates of strain may be simulated by testing at lower rates of strain and lower temperatures. 

Schwakzl, F., and A. J. Staverman Time-temperature dependence of linear viscoelastic behavior. J. Appl. Phys. 23, 838—843 (1952). 

The experimental observation that viscoelastic behavior can be shifted and superimposed, at least to a first approximation, means that all the relaxation processes involved have the same (or nearly the same) temperature dependence. Because the relaxation processes that occur in polymers involve a whole range of length scales, by which we mean they involve coupled motions that range from local rearrangements of just a few chain segments to motions of the chain as a whole, this implies that frictional forces encountered by a chain act in the same or a very similar manner on all the segments. This is important if you intend to be in the business of developing theories of polymer dynamics, but concerns us no further here. 

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