Melting temperature simulation

Typical growth configurations from the simulations are shown in Fig. 4.4, for kT°/s = 0.7 and kT Je = 0.55, respectively (e is the interaction energy between adjacent units, and T° is the equilibrium melting temperature). Notice the increased roughness of the former which has the lower binding energy compared with the temperature. 

Fig. 1 Melting temperatures of polymers k%Tm/Ec) with variable Ev/Ec values. The line is calculated from Eq. 10 and the circles are the simulation results obtained from the onset of crystallization on the cooling curves of disorder parameters, in a short-chain (r = 32) system (occupation density is 0.9375 in a 32-sized cubic box) with a template substrate (Hu and Frenkel, unpublished results)...

Figure 2 shows that, for all but the shortest chains, the Flory-Vrij analysis predicts a slightly higher melting temperature than the present mean-field model. Both approximations are give values higher than the simulation results, but the overall agreement is reasonable. 

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Experimental and simulation results presented below will demonstrate that barrel rotation, the physics used in most texts and the classical extrusion literature, is not equivalent to screw rotation, the physics involved in actual extruders and used as the basis for modeling and simulation in this book. By changing the physics of the problem the dissipation and thus adiabatic temperature increase can be 50% in error for Newtonian fluids. For example, the temperature increase for screw and barrel rotation experiments for a polypropylene glycol fluid is shown in Fig. 7.30. As shown in this figure, the barrel rotation experiments caused the temperature to increase to a higher level as compared to the screw rotation experiments. The analysis presented here focuses on screw rotation analysis, in contrast to the historical analysis using barrel rotation [15-17]. It was pointed out recently by Campbell et al. [59] that the theory for barrel and screw rotation predicts different adiabatic melt temperature increases. 

Figures 10.9S(a,b) show isopleths calculated between (a) corium and siliceous concrete and (b) corium and limestone concrete. Comparison between experimental (Roche et al. 1993) and calculated values for the solidus are in reasonable agreement, but two of the calculated liquidus values are substantially different. However, as the solidus temperature is more critical in the process, the calculations can clearly provide quite good-quality data for use in subsequent process simulations. Solidus values are critical factors in controlling the extent of crust formation between the melt-concrete and melt-atmosphere interface, which can lead to thermal insulation and so produce higher melt temperatures. Also the solidus, and proportions of liquid and solid as a function of temperature, are important input parameters into other software codes which model thermal hydraulic progression and viscosity of the melt (Cole et al. 1984).

Fig. 10.51 Comparison between the calculated (average) and experimental temperatures at five axial positions. The entrance melt temperature was assumed to be 200°C. [Reprinted by permission from T. Ishikawa, S. Kihara, K. Funatsu, T. Amaiwa, and K. Yano, Numerical Simulation and Experimental Verification of Nonisothermal Flow in Counterrotating Nonintermeshing Continuous Mixers, Polym. Eng. Sci., 40, 365 (2000).]...

Fig. 13.10 Filling time versus entrance melt temperature at three constant injection pressures and filling time versus injection pressure at three constant entrance melt temperatures. Mold dimensions are R = 9 cm, H — 0.635 cm. The polymer is unplasticized polyvinyl chloride (PVC) of n = 0.50, m(202°C) = 4 x 104 (N s7m2), A = 6.45 x 10 8, AE = 27.8 (kcal/g mole), p = 1.3 x 103 (kg/m3), Cp — 1.88 x 103 (J/kg K), and k — 9.6 x 10 2 (J/m s K). [Reprinted by permission from R C. Wu, C. F. Huang, and C. G. Gogos, Simulation of the Mold Filling Process, Polym. Eng. Set, 14, 223 (1974).]...

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