Liquid polymers, heat capacity

The reactor system in a pilot plant contains stock tanks that are 24 in in diameter and 36 in high. A relief system must be designed to protect the vessel in the event of fire exposure. The vessel contains a flammable polymer material. What rupture disc diameter is required to relieve the vessel properly Assume a discharge pressure of 10 psig. The molecular weight of the liquid is 162.2, its boiling point is 673°R, the heat of vaporization is 92.4 Btu/lb, and the heat capacity ratio of the vapor is 1.30. 

Figure 11.7 Experimental and calculated heat capacities of solid and liquid PTT [49], From Heat capacity of poly(trimethylene terephthalate), Pyda, M., Boiler, J., Grebowicz, J., Chuah, H., Lebedev, B. V. and Wunderlich, B., J. Polym. Sci., Polym. Phys. Ed., 36, 2499-2511 (1998), Copyright (1998 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc...

When the glass transition temperature of the polymer sample is reached in the DSC experiment, the plot will show an incline. It is obvious that the heat capacity increases at T, and therefore DSC can monitor the of a polymer. Usually the middle of the incline is taken to be the Tg. Above Tg, the polymer chains are much more mobile and thus might move into a more ordered arrangement they may assume crystalline or liquid-crystalline order. When polymers self-or-ganize in that way, they give off heat which can be seen as an exothermal peak in... 

Molar heat capacity of solid and liquid polymers at 25°C ... 

Reliable values for the molar heat capacity in the solid and the liquid state are available for a limited number of polymers only. This emphasizes the importance of correlations between Cp(298) and Cp(298) and the structure of polymers. 

According to this figure a crystalline polymer follows the curve for the solid state to the melting point. At Tm, the value of Cp increases to that of the liquid polymer. The molar heat capacity of an amorphous polymer follows the same curve for the solid up to the glass transition temperature, where the value increases to that of the liquid (rubbery) material. 

In general a polymer sample is neither completely crystalline nor completely amorphous. Therefore, in the temperature region between Tg and Tm the molar heat capacity follows some course between the curves for solid and liquid (as shown in Fig. 5.1 for 65% crystalline polypropylene). This means that published single data for the specific heat capacity of polymers should be regarded with some suspicion. Reliable values can only be derived from the course of the specific heat capacity as a function of temperature for a number of samples. Outstanding work in this field was done by Wunderlich and his co-workers. Especially his reviews of 1970 and 1989 have to be mentioned here. 

Examination of the available literature data showed that, for all the polymers investigated, the curves for the molar heat capacity of solid and liquid might be approximated by straight lines, except for the solid below 150 K. So if the slopes of these lines are known, the heat capacity at an arbitrary temperature may be calculated approximately from its value at 298 K. For a number of polymers the slopes of the heat capacity curves, related to the heat capacity at 298 K, are mentioned in Table 5.3. 

Thermal analysis is capable of providing accurate information on the phase transition temperatures, degradation temperatures, heat capacity, and enthalpy of transition of polymers using comparatively simple DTA, DSC, and TG instruments. The measurement time is short compared with other techniques, such as viscoelastic measurement and nuclear magnetic resonance spectroscopy. Moreover, any kind of material, e.g., powders, flakes, films, fibers, and liquids, may be used. The required amount of sample is small, normally in the range of several milligrams. 

The formation of S o in sulfur melts is a slow reaction, and it takes about 1 h at 160 °C to establish the equilibrium concentration [24, 58]. From the temperature dependence of the polymer content, from the heat capacity Cp of the melt [29] as well as from calorimetric measurements [56, 58] it was concluded that the reaction Ss Sqo is endothermic with an estimated activation energy of ca. 120 kj mor (Ss) [58]. The same value was derived from DSC measurements of liquid sulfur [58]. In this context it was observed that the sudden viscosity increase of liquid sulfur takes place at exactly 159 only if the heating rate approaches zero. If the heating rate is varied between 1.25 and 40 K min higher transition temperatures are observed as the data in Table 1 show [58]. 

The "gas-phase" (fluidized-bed) process is much like the slurry process in that polymer particles are formed at similar temperatures, but a liquid hydrocarbon diluent is not used. A bed of catalyst/polymer is stirred either by mechanical means, or, more often, by fluidization, while ethylene, N2, and other hydrocarbons that act as a coolant are circulated [718-722], Although the "gas phase" process offers many advantages, including the lack of a diluent that can cause polymer swelling, its weak point is poor heat removal from the polymer particles, because of the low heat capacity of a gas. Thus, reactor fouling still occurs,... 

E. Correlation for the heat capacity of "liquid" polymers at room temperature... 

Cp1 Molar heat capacity of "liquid" (molten or rubbery) polymers at constant pressure. 

The heat capacities of polymers can be classified into two types, namely, the heat capacities of "solid" polymers, which will be denoted by Cps, and the heat capacities of "liquid" polymers, which will be denoted by Cp. ... 

Similarly, the heat capacities of both "rubbery" and "molten" polymers can be considered under the category of "liquid" heat capacities. The heat capacity increases discontinuously from its "solid" value to its "liquid" value when an amorphous phase undergoes the glass transition, or when a crystalline phase melts. The jump ACp(Tg) in the heat capacity at the glass transition, which is defined by Equation 4.9, is of considerable interest ... 

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