Dynamic modulus measurement

The strength of the filler skeleton may be characterized by the complex dynamic modulus measured at low frequencies [24]. The authors note that when c > ccr the yield point should be viewed as a sum of two components ... 

The apparatus used by Cramer(Ref 5 ior dynamic modulus measurements was that devised at the US Naval Ordnance Laboratory by Sandler (Ref 2). This apparatus is actually a modification of one described by Meyer Tamm(Ref 1). The instrument used by Cramer is shown schematically in Fig l,p 2 or Ref 5... 

The above expressions confirm the known (Ferry 1980) method of reducing the dynamic modulus measured at different temperatures to an arbitrarily chosen standard temperature Tref, while offering a relatively insignificant improvement on the usual shift coefficient... 

Dynamic Modulus. Measurement of dynamic viscoelasticity was made by the use of a direct-reading dynamic viscoelastometer from the Toyo Measuring Instrument Co., at a frequency of 110 Hz. 

DLUBAC ET AL. Complex Dynamic Modulus Measured hy Three Apparatus 51... 

The variation of the dynamic modulus, measured at 24 °C, and of T with AN content, for all samples tested, is shown in Fig. 31. Both properties increase with increase of AN content, with a rise in modulus of about 20 % and a rise in T of about... 

Now we will discuss a procedure of reconstruction the temperature dependence of the relaxed and unrelaxed elastic moduli. We proposed before that the unrelaxed modulus, which describes the Jahn-Teller contribution, vanishes. Actually, the dynamic modulus measured in an experiment is the total one containing the contribution of the Jahn-Teller system as a summand. So, even the dynamic modulus which contains the unrelaxed Jahn-Teller contribution should be non-zero and can have a certain temperature dependence that is not associated with the Janh-Teller impurities. As well, the relaxed modulus for this reason can differ from one described with the expression (45). To deal with the impurity s contribution only, we can measure the temperature dependence of the dynamic modulus for an un-doped crystal and subtract it from one obtained for the the doped crystal. But it requires two specimens (doped and un-doped) and two experiments. More easy is to reconstruct the relaxed and unrelaxed moduli with the help of the data relating to the doped crystal. To derive the necessary expressions we will use the (20) and (21) and... 

Warley, R. L. Feke, D. L. Manas-Zloczower, I., Transient Effects in Dynamic Modulus Measurements of Silicone Elastomers. 1. Zero Mean Strain Measurements. J. Appl. Polym. Sci. 2005, 98,1001-1009. 

Fig. 2.28. A plot of tan 3 as a function of actual frequencies at several temperatures for NBS-PIB. The data were obtained by using several instruments spanning the frequency range as shown in the abscissa. The high-frequency data at -35.8 °C (open circles) are from Fitzgerald et al, J. Appl. Phys. 24 (1953), 640. The rest of the data were obtained by a combination of creep-compliance and dynamic-modulus measurements [209]. From Plazek et al. by permission [209].

Dynamic modulus measurements were made over the temperature range of -50 C to 30°C, and the frequency range of 0.02 to... 

Dynamic mechanical measurements were made on PTEE samples saturated with various halocarbons (88). The peaks in loss modulus associated with the amorphous relaxation near —90°C and the crystalline relaxation near room temperature were not affected by these additives. An additional loss peak appeared near —30° C, and the modulus was reduced at all higher temperatures. The amorphous relaxation that appears as a peak in the loss compliance at 134°C is shifted to 45—70°C in the swollen samples. 

Similar information can be obtained from analysis by dynamic mechanical thermal analysis (dmta). Dmta measures the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping are deterrnined from such measurements. Detailed information on the theory of dmta is given (128). 

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. 

However, it yields dynamic modulus. Some other techniques were also used to characterize hydrogels, for example, viscoelastic measurements [28, 30, 31] and swelling equilibrium [20]. 

Fig. 10. Concentration dependence of a modulus in the region of low-frequency plateau (i.e. yield stress , measured by a dynamic modulus). Dispersion medium poly (butadiene) with M = 1.35 x 105 (7), silicone oil (2) polybutadiene with M = 1 x I04 (3). The points are taken from Ref. [6], The straight line through these points is drawn by the author of the present paper. In the original work the points are connected by a curve in another manner...

The existence of the G (A) dependence even in the region of very small amplitudes is explained by a brittle pattern of fracture of a filler s structure, so that measuring virtually frequency (and amplitude) dependences of a dynamic modulus, a researcher always deals with a material in which the structure is partially fractured. 

The discussion of the results of measuring the dynamic properties of filled polymers is based very often on the idea of correlation of the G" and t functions, which is not always expressed directly. However, due to a very sharp dependence of a dynamic modulus on the amplitude, it is not clear how to understand this correlation. 

Moreover, if for pure polymer melts the correlation of the behavior of the functions ri (co) andrify) under the condition of comparing as y takes place, as a general rule, but for filled polymers such correlation vanishes. Therefore the results of measuring frequency dependences of a dynamic modulus or dynamic viscosity should not be compared with the behavior of the material during steady flow. 

A technique for performing dynamic mechanical measurements in which the sample is oscillated mechanically at a fixed frequency. Storage modulus and damping are calculated from the applied strain and the resultant stress and shift in phase angle. 

Experimentally DMTA is carried out on a small specimen of polymer held in a temperature-controlled chamber. The specimen is subjected to a sinusoidal mechanical loading (stress), which induces a corresponding extension (strain) in the material. The technique of DMTA essentially uses these measurements to evaluate a property known as the complex dynamic modulus, , which is resolved into two component parts, the storage modulus, E and the loss modulus, E . Mathematically these moduli are out of phase by an angle 5, the ratio of these moduli being defined as tan 5, Le. 

The linear visco-elastic range ends when the elastic modulus G starts to fall off with the further increase of the strain amplitude. This value is called the critical amplitude yi This is the maximum amplitude that can be used for non-destructive dynamic oscillation measurements... 

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

An apparatus for measuring the dynamic modulus and hysteresis of elastomers. The stress-strain oscillogram is shown on a ground-glass screen by means of an optical system. Now superseded by modem computer controlled servo hydraulic and dynamic mechanical thermal analysis machines. Roll Bending... 

Dynamic rheological measurements have recently been used to accurately determine the gel point (79). Winter and Chambon (20) have determined that at the gel point, where a macromolecule spans the entire sample size, the elastic modulus (G ) and the viscous modulus (G") both exhibit the same power law dependence with respect to the frequency of oscillation. These expressions for the dynamic moduli at the gel point are as follows ... 

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