Properties viscoelastic

The viscoelastic properties such as storage modulus, loss modulus, and tan 8 are measured using a dynamic mechanical analyzer (DMA) and/or a rheometer. 

Similar to Wu and Liao (75), Wu et al. (74) used a DMA (Model -242C, NETZSCH Co.) and a rheometer (HAAKE RS600, Thermo Electron Co.) to evaluate the viscoelastic behavior of the carboxylic-acid-functionalized MWCNTs reinforced PCL/PLA blend. Using DMA, it was observed that, with the increase of MWCNT loading, the Tg of the blend system shifted to higher temperatures. This agrees with the results obtained from the other studies discussed above and indicates the MWCNTs are compatible with the blend. The viscoelastic properties observed via rheometer were similar to those by Wu et al. (73), discussed above. 

The viscoelastic properties of liquid crystals are very important, and mainly determine the behavior of liquid crystals in external electric fields, defining such characteristics as controlling voltages, steepness of the transmission-voltage curve, response times, etc. Now only the phenomenological theory of the viscoelastic properties of nematic liquid crystals is essentially complete [18, 28]. 

We will also describe the main methods for the measurement of these parameters. 

The measurement of rheological properties of the PLFNCs in the molten state is crucial in order to gain a fundamental understanding of the nature of the processability and the structure-property relationships for these materials. 

Dynamic oscillatory shear measurements of polymeric materials are generally performed by applying a time dependent strain of y(t) = y0sin(cot) and the resultant shear stress is a(t) = y0[G sin(a)t) + G cos(cot)], with G and G being the storage and loss modulus, respectively. 

Generally, the rheology of polymer melts depends strongly on the temperature at which the measurement is carried out. It is well known that for thermorheological simplicity, isotherms of storage modulus (G (co)), loss modulus (G ( d)) and complex viscosity (r (co)) can be superimposed by horizontal shifts along the frequency axis  

In the case of polymer samples, it is expected that, at the temperatures and frequencies at which the rheological measurements were carried out, the polymer chains should be fully relaxed and exhibit characteristic homo-polymer-like terminal flow behavior (i.e., the curves can be expressed by a power-law of G oc co2 and G oc co). 

The rheological properties of insitu polymerized nanocomposites with end-tethered polymer chains were first described by Krisnamoorti and Giannelis [33]. The flow behavior of PCL- and Nylon 6-based nanocomposites differed extremely from that of the corresponding neat matrices, whereas the thermorheological properties of the nanocomposites were entirely determined by the behavior of the matrices [33]. The slope of G (co) and G (co) versus flxco is much smaller than 2 and 1, respectively. Values of 2 and 1 are expected for linear mono-dispersed polymer melts, and the large deviation, especially in the presence of a very small amount of layered silicate loading, may be due to the formation of a network structure in the molten 

Most pigmented systems are considered viscoelastic. At low shear rates and slow deformation, these systems are largely viscous. As the rate of deformation or shear rate increases, however, the viscous response cannot keep up, and the elasticity of the material increases. There is a certain amount of emphasis on viscoelastic behavior in connection with pigment dispersion as well as ink transportation and transformation processes in high-speed printing machines (see below). Under periodic strain, a viscoelastic material will behave as an elastic solid if the time scale of the experiment approaches the time required for the system to respond, i.e., the relaxation time. Elastic response can be visualized as a failure of the material to flow quickly enough to keep up with extremely short and fast stress/strain periods. 

The viscoelastic behavior of a printing ink or other material is largely a function of the polarity of pigment and medium [118]. However, it is difficult to quan- 

There are limited measurements of the viscoelastic properties of hard-sphere colloids at elevated shear rates, stresses, and frequencies, de Kruif, et al. report rir of silica spheres in the small and large shear-rate limits, as functions of / (53). At smaller concentrations, rjr depends but weakly on /c. Above p 0.4, shear thinning becomes apparent, de Kruif, et al. propose that r]r diverges 2 — 4 /4 m), with 4 m being 0.71 or 0.63 in the large and small shear limits. Jones, et al. also find weak shear thinning for (p 0.395, the extent of shear thinning increases quite substantially for volume fractions between 0.59 and 0.60(55). 

measured viscosity as affected by shear rate for silica sphere suspensions, finding shear thinning at lower shear rates(57). In some but not all systems and volume fractions above 0.5, a reproducible abrupt transition to shear tbickening was found at elevated shear rates. The transition shear rate depended on concentration and temperature. In contrast, Jones, et al plot only a shear thinning region. A possible explanation for this difference is provided by the Peclet number Pe, 

We now consider the frequency dependence of the dynamic moduli. An ansatz for the viscoelastic moduli of polymer solutions is presented where it naturally appears, early in Chapter 13. Anticipating those results, the predictions of that ansatz are(58) 

Treatments such as mercerization/acetylation of fibers will result in an increase in the dynamic mechanical properties of composites, which was observed by Martins and Mattoso [40]. The stabilizing effect of lignin filler on NR was examined by Kosikova et al. [41], using DMA. Addition of hgnin improved the dynamic mechanical properties of NR vulcanizates. In another study. Da Costa et al. [27] found that addition of RHA to NR causes a shift in Tg values of filled mbber vulcanizates toward higher temperatures, showing the presence of cross-Unks, 

The viscoelastic properties of short melamine fiber-reinforced NBR composites were studied by Rajeev et al. [43]. Usage of resorcinol-hexa-siHca bonding system in the composites also causes a significant improvement in the storage and loss modulus values. 

As shown in Chapter 10, molecular dynamics in polymers is characterized by localised and cooperative motions that are responsible for the existence of different relaxations (ot, p, y). These, in turn, are responsible for energy dissipation, mechanical damping, mechanical transitions and, more generally, of what is called a viscoelastic behavior - intermediary between an elastic solid and a viscous liquid (Ferry, 1961 McCrum et ai, 1967). 

Let us remind ourselves that for a purely elastic solid a = Ee, where E is independent of e, whereas for a purely viscous (Newtonian) liquid s = Tiy, where p (viscosity) is independent of y (shear rate). 

A viscoelastic solid is characterized by the fact that its modulus E is a function of time. Thus, the response of the material to a loading program, s(t) or a(t) needs the application of the Boltzmann superposition principle (Sec. 11.1). In the case of programmed strain  

These relationships show that to model the mechanical behavior of a given viscoelastic material we need to know the function(s) describing the time variation E(t), G(t), D(t), J(t) of the moduli or compliances under consideration. 

One of the relationships mostly used in this domain is the Kolrausch-Williams-Watt (KWW) equation  

Another way to locdt at this is to consider that the polymer exhibits a characteristic relaxation time, t. If the stress is applied for a time period Ts that is much 

Even though these transitions are different in many ways, as demonstrated below, the way in which acoustic energy interacts with polymeric materials permits us to use AW devices to probe changes in polymer film viscoelastic properties associated with these transitions. It should be emphasized up front, however, that evaluating the viscoelastic properties (e.g., modulus values) requires an ability to effectively model the film displacement profiles in the viscoelastic layer. As described in Section 3.1.8, the film displacement effects are dictated by the phase shift, f , across the film. Since f depends on film thickness, perturbations in acoustic wave properties due to changes in viscoelastic properties (e.g., during polymer transitions) do not typically depend simply on the intrinsic polymer properties. This can lead to erroneous predictions if the film 

The attenuation and velocity of acoustic energy in polymers are very different from those in other materials due to their unique viscoelastic properties. The use of ultrasonic techniques, such as acoustic spectroscopy, for the characterization of polymers has been demonstrated [47,48]. For AW devices, the propagation of an acoustic wave in a substrate causes an oscillating displacement of particles on the substrate surface. For a medium in intimate contact with the substrate, the horizontal component of this motion produces a shearing force. In such cases, there can be sufficient interaction between the acoustic wave and the adjacent medium to perturb the properties of the wave. For polymeric materials, attenuation and velocity of the acoustic wave will be affected by changes in the viscoelastic behavior of the polymer. 

Because of the oscillatory nature of the acoustic wave, probing of polymer viscoelastic properties using AW devices is analogous to the high rate/short time scale probing of polymers mentioned previously. The wave period, which is the inverse of the AW frequency, determines the time scale of the applied strain. Wave attenuation and velocity, or resonant amplitude and frequency, can be monitored at a relatively fixed frequency (rate) while scanning the temperature. 

In this section we will describe how a proper accounting for film dynamics, based on a model of the thin-film/acoustic-wave interactions, can be used to quantitatively evaluate the shear modulus values as a function of temperature. As described in Section 3.1, an equivalent-circuit model can be used to relate the measured TSM electrical characteristics to the elastic properties, density, and thickness of a polymer film coating the device. Consequently, measurements made with polymer-coated TSM devices can be used to extract the shear elastic properties of the film. 

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The Computation of Polymeric Material s Viscoelastic Properties by Dynamic Indentation Method. 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

Polymers owe much of their attractiveness to their ease of processing. In many important teclmiques, such as injection moulding, fibre spinning and film fonnation, polymers are processed in the melt, so that their flow behaviour is of paramount importance. Because of the viscoelastic properties of polymers, their flow behaviour is much more complex than that of Newtonian liquids for which the viscosity is the only essential parameter. In polymer melts, the recoverable shear compliance, which relates to the elastic forces, is used in addition to the viscosity in the description of flow [48]. 

Ferry J D 1980 Viscoelastic Properties of Polymers (New York Wiley)... 

Ferry, J. D., Viscoelastic Properties of Polymers, Wiley, New York, 1980. 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

In principle, the relaxation spectrum H(r) describes the distribution of relaxation times which characterizes a sample. If such a distribution function can be determined from one type of deformation experiment, it can be used to evaluate the modulus or compliance in experiments involving other modes of deformation. In this sense it embodies the key features of the viscoelastic response of a spectrum. Methods for finding a function H(r) which is compatible with experimental results are discussed in Ferry s Viscoelastic Properties of Polymers. In Sec. 3.12 we shall see how a molecular model for viscoelasticity can be used as a source of information concerning the relaxation spectrum. 

In other work, the impact of thermal processing on linewidth variation was examined and interpreted in terms of how the resist s varying viscoelastic properties influence acid diffusion (105). The authors observed two distinct behaviors, above and below the resist film s glass transition. For example, a plot of the rate of deprotection as a function of post-exposure processing temperature show a change in slope very close to the T of the resist. Process latitude was improved and linewidth variation was naininiized when the temperature of post-exposure processing was below the film s T. 

International Rubber Hardness. The International mbber hardness test (ASTM D1415) (2) for elastomers is similar to the Rockwell test ia that the measured property is the difference ia penetration of a standard steel ball between minor and major loads. The viscoelastic properties of elastomers require that a load appHcation time, usually 30 seconds, be a part of the test procedure. The hardness number is read directly on a scale of 0 to 100 upon return to the minor load. International mbber hardness numbers are often considered equivalent to Durometer hardness numbers but differences ia iadenters, loads, and test time preclude such a relationship. 

Detailed treatments of the rheology of various dispersed systems are available (71—73), as are reviews of the viscous and elastic behavior of dispersions (74,75), of the flow properties of concentrated suspensions (75—82), and of viscoelastic properties (83—85). References are also available that deal with blood red ceU suspensions (69,70,86). 

Fig. 21. Dynamic viscoelastic properties of a low density polyethylene (LDPE) at 150°C complex dynamic viscosity Tj, storage modulus G and loss modulus G" vs angular velocity, CO. To convert Pa-s to P, multiply by 10 to convert Pa to dyn/cm, multiply by 10.

Tensile Testing. The most widely used instmment for measuring the viscoelastic properties of soHds is the tensile tester or stress—strain instmment, which extends a sample at constant rate and records the stress. Creep and stress—relaxation can also be measured. Numerous commercial instmments of various sizes and capacities are available. They vary greatiy in terms of automation, from manually operated to completely computer controlled. Some have temperature chambers, which allow measurements over a range of temperatures. Manufacturers include Instron, MTS, Tinius Olsen, Apphed Test Systems, Thwing-Albert, Shimadzu, GRC Instmments, SATEC Systems, Inc., and Monsanto. 

A typical stress—strain curve generated by a tensile tester is shown in Eigure 41. Creep and stress—relaxation results are essentially the same as those described above. Regarding stress—strain diagrams and from the standpoint of measuring viscoelastic properties, the early part of the curve, ie, the region... 

Acoustic Measurements. Measurement of the propagation of ultrasonic acoustic waves has been found useful for determining the viscoelastic properties of thin films of adhesives. In this method, the specimen is clamped between transmitting and receiving transducers. The change in pulse shape between successive reverberation of the pulse is dependent on the viscoelastic properties of the transmitting material. Modulus values can be calculated (267,268). 

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

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