Example calculations melt viscosity

Tests of linear, quadratic, and higher order polynomials have been applied to a wide variety of tabulated data available from the literature. A multiple linear regression model has been found to yield a better fit than simple polynomials in many cases. Intersection points yield transition temperatures or pressures, as the case may be. Examples of melt viscosity data will be discussed in this paper. Residuals analysis and the magnitude of the calculated standard error are used as descriptors of the goodness of fit for the statistical tests. The judicious use of derivative treatments on dielectric and dynamic mechanical relaxation data to enhance weak liquid state damping processes is also presented. 

The value of is dependent on the type of viscosity measured. For example, =0.745 for nylon-6,6 in formic acidiflimiting viscosity number data are calculated from solution viscosities. However, =ca 3.5 for this nylon if melt viscosity data are used. 

Example 9.6 Melting in Screw Extruders The screw geometry and operating conditions for the LDPE extrusion experiment (Figs. 9.24 and 9.36) were given in Example 9.5. Calculate the SBP, using the Power Law model with temperature-dependent viscosity and linear temperature prohle. 

Example 9.8 The Melting Rate in a Co-rotating Disk Chamber In this example we calculate the rate of melting of LDPE in a parallel chamber of width 0.75 in, outer radius of 3.75 in, inner radius 2.25 in as a function of disk speed with disk temperature set at 450°F. The viscosity is 0.035 lbfs/in2, the melting point is 231°F, the heat of fusion is 55.8 Btu/lb, the thermal conductivity of the melt is 0.105 Btu/ft°F-h, the specific heat of the melt and solids are 0.62 and 0.66 Btu/lb°F, respectively, and the solids and melt densities are 57 and 48 lb/ft3, respectively. 

From the correspondence between the calculated and experimental curves we can extract other information. For example the temperature (ca. 72 °C) at which x = 1/2 is shown on Fig. 14b. Above this temperature no more chains break at this temperature and higher, the craze growth is disentanglement dominated. We can use the fact that = 1/2 and Eq. (19) to extract a value for the corresponding to disentanglement of chains at the void interface under these conditions this value is 1.5 x 10" N-s/m, a value that is only reached for polystyrene melts (from zero shear viscosity or diffusion measurements) at a temperature of about 120 °C, or 20° above T. ... 

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... 

Many of the commercial reactants used in urethane synthesis are impure materials, for example MDI may be used as pure MDI, a low melting-point (38°C) solid polymeric or crude MDI, which is a dark-coloured low viscosity liquid. Alternatively, MDI and TDI prepolymers may be blended and perhaps have various additives incorporated, all of which may affect the final quantity of free NCO available for reaction. Also, active isocyanate content of a prepolymer decreases with storage, a decrease of about 0-05% per month being normal. For these reasons it is necessary to measure and specify the amount of isocyanate available for reaction at any specific time, and this is done by calculation of the isocyanate equivalent weight of the mixture using the following procedure ... 

The quantity RllM Y is Rg in A, a measure of chain stiffness. For example, polycarbonate, with (RpM y = 0.457, is stiffer than polystyrene, which has a value of 0.275. The importance of these quantities lies in their relation to physical and mechanical behavior. Both melt and solution viscosities depend directly on the radius of gyration of the polymer and on the chain s capability of being deformed. The theory of the random coU (Section 5.3), strongly supported by these measurements, is used in rubber elasticity theory (Chapter 9) and many mechanical and relaxation calculations. 

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