Viscoelastic properties, measurement

As an example of the concentration dependence of viscoelastic properties in Fig. 16.11 the shear creep compliance of poly(vinyl acetate) is plotted vs. time for solutions of poly(vinyl acetate) in diethyl phthalate with indicated volume fractions of polymer, reduced to 40 °C with the aid of the time temperature superposition principle (Oyanagi and Ferry, 1966). From this figure it becomes clear that the curves are parallel. We may conclude that the various may be shifted over the time axis to one curve, e.g. to the curve for pure polymer. In general it appears that viscoelastic properties measured at various concentrations may be reduced to one single curve at one concentration with the aid of a time-concentration superposition principle, which resembles the time-temperature superposition principle (see, e.g. Ferry, General references, 1980, Chap. 17). The Doolittle equation reads for this reduction ... 

Conclusions. Results from the biocompatibility studies in rabbit supratellar bursa, measurement of hydrophilic properties, lubrication and wear in-vitro studies, determination of viscoelastic properties, measurement of damping coefficient and impact test, total elbow joint replacement design and in-vivo percutaneous implant experiment, all indicate that this series of polyurethanes is an excellent candidate biomaterial for the prosthetic replacement of articular cartilage, artificial joint prostheses and percutaneous implantable devices. 

Thus, for a more complete understanding of bone s response to applied loads, it is important to know its rheologic properties. There have been a number of early studies of the viscoelastic properties of various long bones [Sedlin, 1965 Smith and Keiper, 1965 Lugassy, 1968 Black and Korostoff, 1973 Laird and Kingsbury, 1973]. However, none of these was performed over a wide enough range of frequency (or time) to completely define the viscoelastic properties measured, for example, creep or stress relaxation. Thus it is not possible to mathematically transform one property into any other to compare results of three different experiments on different bones [Lakes and Katz, 1974]. 

Poly(trimethylene succinate) 1-7 viscoelastic properties measured and compared with theory. Kx measured, compared with theory RIS treatment [204]... 

Because of the frequency dependence of Tg, the convention adopted for assignment of the glass transition temperature is an important consideration. Traditionally, a frequency of 1 Hz has been used as a standard value. This is based on the historic precedence, since the torsion pendulum was the most widely used DMA technique in the early days of viscoelastic property measurements. The torsion pendulum is a free vibration technique with a natural frequency of approximately 1 Hz. The 1 Hz value also is reasonably close (within 10 °C) to the Tg values determined by other widely used methods such as DSC, dilatometry, and TMA. The relation between DMA and DSC Tg values is considered further at the end of this chapter (Sircar and Drake 1990). Because of the ambiguity inherent in the kinetic nature of Tg, it is most important that the test frequency be reported along with any Tg value determined by a DMA technique. 

It should be noted that the temperature coefficient of longitudinal wave velocity may change abruptly at the glass transition temperature owing purely to the change in thermal expansion coefficient (since it depends on the density as well as the viscoelastic properties) this does not represent any discontinuity in the viscoelastic properties measured at high frequency." ... 

In this work, the adhesive tensile properties were not measured directly. The equation was used to allow prediction of the peel results, with the material parameters being derived from the linear viscoelastic property measurements. 

As stated previously, the maximum relaxation time becomes infinite approaching the gel point. Specifically evaluating gelation from the viewpoint of dynamic structure requires measurements for infinite time. Also, the strain y must be very close to zero to avoid damage on the crosslinks, because the crosslink density of the networks at the gel point is extremely small. In practice, when the gel point is studied by viscoelastic property measurements, it is assumed that all relaxation modes will appear in the relaxation spectrum [31]. Under this hypothesis, the stress relaxation modulus G t) can be expressed as G t) t L The exponential rule will also apply for the complex modulus. That is. 

In order to determine the viscoelastic properties of silicone gel materials, vibrational measurement techniques are used. The principle of vibrational measurement techniques involves determining die viscoelastic quantities by observing the responding mechanical behavior when cyclic deformation is applied repeatedly. Dynamic viscoelastic property measurements are performed with a dynamic mechanical spectrometer such as the RDA-II from Rheometrics. This instrument measures the complex modulus G and loss factor tan S from the torque measured by the transducer equipped at the upper portion of the sample chamber when shear deformation is applied to the sample at a specified shear strain and frequency from the actuator at the bottom of the sample chamber. 

Green MA, Bilston LE, Sinkus R (2008) In vivo brain viscoelastic properties measured by magnetic resonance elastc raphy. NMR Bio-med 21 755-764... 

Tchir, W. J., Saucier, P. C. Accuracy in linear viscoelastic property measurement Effects of instrument comphance andinertia revisited. Proc. Ann. Tech. Conf. (ANTEC) Soc. Plastics. Engrs., Tech. Papers (1994) 40, pp. 1205-1210... 

Agee, B. L. and L. D. Mitchell, Frequency dependent viscoelastic property measurement via modal analysis techniques, 9th International Conference on Experimental Mechanics, Copenhagen, Denmark, pp. 1978-1988, 1990. 

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. 

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. 

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). 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

Viscoelastic phenomena always involve the change of properties with time and, therefore, the measurements of viscoelastic properties of solid polymers may be called dynamic mechanical. Dynamic mechanical thermal analysis (DMTA) is a very useful tool for studying... 

Thermal and thermomechanical analyses44 are very important for determining die upper and lower usage temperature of polymeric materials as well as showing how they behave between diose temperature extremes. An especially useful thermal technique for polyurethanes is dynamic mechanical analysis (DMA).45 Uiis is used to study dynamic viscoelastic properties and measures die ability to... 

Dynamic mechanical measurements for elastomers that cover wide ranges of frequency and temperature are rather scarce. Payne and Scott [12] carried out extensive measurements of /a and /x" for unvulcanized natural mbber as a function of test frequency (Figure 1.8). He showed that the experimental relations at different temperatures could be superposed to yield master curves, as shown in Figure 1.9, using the WLF frequency-temperature equivalence, Equation 1.11. The same shift factors, log Ox. were used for both experimental quantities, /x and /x". Successful superposition in both cases confirms that the dependence of the viscoelastic properties of rubber on frequency and temperature arises from changes in the rate of Brownian motion of molecular segments with temperature. 

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