Loss angle

Dissipation factor (loss tangent) lEC 250. As explained in the chapter, this is the tangent of the dielectric loss angle and is now more commonly used than the power factor, which is the sine of the loss angle. When the angle is small the two are almost identical (e.g. for a loss angle of 10° the difference is about 1.5%). 

Typically, large-scale gas filling makes the main characteristics of foam plastics — coefficients of heat and temperature conductivity, dielectric permeability, and the tangent of the dielectric loss angle — totally independent of the chemical structure of the original polymer [1],... 

The dissipation factor is a ratio of the real power (in-phase power) to the reactive power (power 90° out of phase). It is also defined as (1) IT is the ratio of conductance of a capacitor in which the material is the dielectric to its susceptance, (2) IT is the ratio of its parallel reactance to its parallel resistance it is the tangent of the loss angle and the cotangent... 

The variations of dielectric constant and of the tangent of the dielectric-loss angle with time provide information on the mobility and concentration of charge carriers, the dissociation of defect clusters, the occurrence of phase transitions and the formation of solid solutions. Techniques and the interpretation of results for sodium azide are described by Ellis and Hall [372]. 

So in order to minimize this noise one possibility is to work at low temperature, this is what is done in the Japanese TAMA project. The other solution is to use optical materials with a low value of the loss angle, or equivalently a high quality factor. 

The incorporation of reinforcing hllers into rubber results in most cases in an increase of the storage and loss moduli, G and G", and an increase in hysteresis, as quantihed by the loss angle 8, where tan 8 is C jG. When properly dispersed and coupled to the mbber matrix via a coupling agent, as represented by a low Payne effect, silica also shows less hysteretic loss at elevated temperatures. 

Figure 3.25 Storage modulus, elastic modulus, and loss angle for a cone and plate rheological measurement. The data are for a GPPS resin with an MFR of 1.5 dg/min (5 kg, 200°C) measured at 225°C...

Here t is the resulting shear stress, 6 is the phase shift often represented as tan(d), and (O is the frequency. The term 6 is often referred to as the loss angle. The in-phase elastic portion of the stress is To(cosd)sin(wt), and the out-of-phase viscous portion of the stress is To(sind)cos(complex modulus and viscosity, which can be used to extend the range of the data using the cone and plate rheometer [6] ... 

Tangent of the loss angle and the cotangent of the phase angle... 

The loss tangent is an important quantity. The product of the loss tangent and the dielectric constant, tan 5, is called the loss factor and is the primary criterion for judging the usefulness of a dielectric as an insulator material. For this purpose, it is desirable to have a low dielectric constant and a small loss angle. For applications in which it is desirable to obtain a high capacitance in the smallest physical space, a high dielectric constant must be used, and a low value of the loss angle is needed. 

Dielectric loss angle (symbol 5) An angle between the vector for the amplitude of the total current and that for the amplitude of the charging... 

Eqs. (1.16) are, of course, very well-known. G is known as the storage modulus in shear. It describes that part of the shear stress, which is in phase with the deformation. G" is the loss modulus in shear. It describes that part of shear stress which is 90 degrees out of phase. 6 is the loss angle. These definitions will be used occasionally in this review. 

Fig. 2.4. Doubled extinction angle 2% vs. shear rate (open circles) and loss angle <5 vs. angular frequency (closed circles) for the melt of anionic polystyrene Sill at a measurement temperature of 196° C [Wales, Den Otter (56)]...

Anionic polystyrene Sill seems to be a suitable polymer for this type of investigation. Some solution properties of this polymer have already been discussed in the previous chapter. Fig. 2.4 gives some properties of the melt of this polymer at a measurement temperature of 196° C (56). In this figure the doubled extinction angle 2% as a function of shear rate q (open circles) is compared with the loss angle d as a function of angular frequency (closed circles). In accordance with eq. (2.22) the initial slopes of these curves coincide. This coincidence, however, appears to persist even into the non-linear part of the functions. Such a persistence... 

Fig. 4.6. Doubled extinction angle 2y (closed triangles) and doubled orientation angle 2% (open circles and triangles) as function of shear rate q, and loss angle 6 as a function of angular frequency (closed circles, connected by dashed lines) for the melts of two polypropylene samples. Data of samples are given in Table 3.3. Measurement temperature 210° C (36)...

Dynamic mechanical analysers, as discussed in chapter 9, can be constructed so that they can be used with unvulcanised materials and, hence, the in phase and out of phase components of modulus and the loss angle measured. The usual test piece geometries for cured rubbers are not convenient for the uncured materials where some form of oscillating shear is probably the best approach. This is the geometry used in cure meters discussed in the next section and such instruments have formed the basis for apparatus which measures dynamic properties from before and through the curing process. 

Figure 9-2. Sinusoidal stain and stress cycles. I strain, amplitude a II in-phase stress, amplitude b III out-of-phase stress, amplitude c IV total stress (resultant of II and III, amplitude d. a is the loss angle...

The power factor of a material may be described loosely as the fraction of the electrical energy stored by the condenser in each cycle which is lost as heat. This arises because the phase difference between voltage and current deviates from 90° (which it would be for a perfect dielectric, e.g. vacuum) by the loss angle, 8. The dissipation factor is the tangent of the loss angle, tan 8. 

---