Rheological force

The viscosities of polymer melts, calculated from the storage modulus and the loss modulus, have to be within a range to resist the applied forces, which act against the rheological forces. But they should not be as large as to prevent the necessary deformation before the start of sodification. The elastic part of deformation has to be small since an elastic deformation happens more rapidly than a viscous one. Therefore, a considerable elastic deformation can lead to a cohesive fracture of the fiber in the molten state. The ratio of the viscous to the elastic energy of the polymer melt may be seen as one of the most important factors for the spinnability of polymers. For the usual commercially used spinnable polymers, such as, for example, poly(ethylene terephthalate), the ratio is about G"/G >10... 

FIGURE 12.34 Rheological force versus jet stretch at different spin-bath conditions. Spinneret diameter was 0.0127 cm (5 mils) and the plug flow velocity within the spinneret was 16.62cm/s. The concentration of sodium thiocyanate (NaSCN) in the bath and the bath temperature are given. (From Han, C.D. and Segal, L., /. Afip/. Polym. Sci. 14, 2973, 1970.)... 

The maximum take-up velocity is very reproducible and depends essentially on every process variable, e.g., polymer composition and molecular weight, spinning dope composition, bath composition, bath temperature, spinneret capillary diameter, and flow rate. A parameter that seems to determine the upper limit in take-up velocity is the free velocity, Vf [244,323]. Recall that the free velocity is the velocity at which the filament leaves the spinneret under zero tension. The free velocity will increase in an approximately linear manner with the volumetric flow rate through the capillary, and at a fixed flow rate it will increase as the capillary diameter is decreased. When the take-up velocity, Fi, is increased while Ff is held constant, the magnitude of the rheological force, F(rheo), will increase until the filament breaks at the spinneret face. 

The values of the rheological force being determined by the rate gradient, it was concludent that it plays a special part in mechano-destruction processes. 

In the drawdown section, the attenuation air is used to speed the filaments. The shear forces between the attenuation air and the filaments result in filament speed. The filaments are attenuated in a drawdown zone close to the filament exit from the die face. In the first part of the drawdown zone, the filament diameter is decreasing linearly. At the end of this drawdown zone, the drawdown point is achieved and the filament diameter is drawn to its final diameter very rapidly. Since this draw point is physically located somewhere in the cooling chamber, it is obvious that the filaments in the quench chamber are moving faster than the surrounding air stream, so the forces created by the attenuation air are necessary to overcome the shear forces created by pulling fast filaments though slow air zones and the rheological forces out of the filaments. 

Compared with F it is more convenient to measure the rheological force at the take-up device, i.e., z = L, where L is the distance between the take-up device and the spinneret. Therefore, the rheological force at a given point can be given by ... 

By using Equation 9.13, the rheological force at a given point in the spinning filament can be calculated from measurable quantities. The gradient of axial tension along the spiiming filament can be obtained from ... 

Figure 13.2. Schematic of the path of a liquid jet ejected from the nozzle tip during centrifugal spinning. Rheological force, surface tension and gravitational force may affect the nanofiber formation process, but they are not shown here for the purpose of simplicity.

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