Ceiling temperature defined

The entropy term is negative so that it is the enthalpy or energy term that drives the polymerization. At low temperatures, the enthalpy term is larger than the TASp term so that polymer growth occurs. At some temperature, called the ceiling temperature, the enthalpy and the entropy terms are the same and AGp = 0. Above this temperature depolymerization occurs more rapidly than polymer formation so that polymer formation does not occur. At the ceiling temperature depolymerization and polymerization rates are equal. The ceiling temperature is then defined as... 

The latter are plausible approximations because at the transition temperature, and above it, the initial monomer concentration, M0, is nearly equal to its equilibrium concentration, i.e. M0m Me jK. In view of the last relation, the ceiling temperature of the system is defined as the temperature at which K(T) = 1/M0. 

Equation 3 shows that for a given monomer concentration [M]eq at temperatures above a critical value Tc the rate of the depolymerization step becomes greater than the rate of the polymerization step and dominates the reaction. The critical temperature Tc is called ceiling temperature (22, 23). (AH is the enthalpy of polymerization, and AS° is the entropy of polymerization at the monomer concentration [M] = 1 mole/liter.) The concentration of the monomer at equilibrium [M]eq is identical to the equilibrium constant K, which is defined by the rate constants kp and kd. 

From the practical point of view, the glass transition is a key property since it corresponds to the short-term ceiling temperature above which there is a catastrophic softening of the material. For amorphous polymers in general, and thus for thermosets, one can consider that the glass transition temperature, Tg, is related to the conventional heat deflection temperature (HDT) (usually, HDT is 10-15°C below Tg, depending on the applied stress and the criterion selected to define Tg). 

In view of thermodynamics the ceiling temperature looks like a melting point. Below and above this temperature the system consists of 100% polymer and of 100% monomer, respectively. This is shown in Fig. 20.2. If, however, the polymer is soluble in its monomer, then the free enthalpy of mixing also plays a role and the result will be that the "melting point" is not as sharp as shown there will be a gradual change (i.e. the dashed line) from 100% polymer to 100% monomer. The ceiling temperature is in this case defined as the temperature where the amount of monomer equals the amount of polymer (i.e. at 50%) and equal to (see, e.g. Ivin, 2000) ... 

The fourth major parameter which defines a system after the monomer, the initiator(s) and the solvent, is the temperature at which the polymerisation is conducted. The effect of temperature upon the position of the propagation-depropa tion equilibrium (ceiling temperature) is not directly relevant and too well-known to be discus here. We are obviously more interested in discussing the specific role of temperature in the reactions leading to the formation of chain carriers. The following considerations are pertinent to the kinetics of such interactions and to the thermodynamics of the reailting equflibria. 

The ceiling temperature is therefore defined as the temperature at which the rates of propagation and depolymerization are equal. For that reason, is a threshold temperature above which a specific polymer cannot exist. Representative values of for some common monomers are given in Table 14.23. 

For a pyrolytic process, the temperature T satisfying relation (7) is defined as the ceiling temperature T ... 

The ceiling temperature can also be defined as the temperature, above which the formation of long-chain polymer from monomer, at concentration is impossible. At this temperature the free... 

A ceiling pressure can be defined in analogy to the ceiling temperature. Above the ceiling pressure, temperature being constant, polymerization is no longer possible. This pressure is, for example, about 0.2 kbar at 25 C for the polymerization of 0.1 mol/liter chloral in pyridine, 5 kbar for pure butyr-aldehyde, and over 30 kbar for pure carbon disulfide. 

This equation can also be rearranged to define the ceiling temperature Tc at which the polymerization rate becomes zero for a given monomer concentration ... 

At equilibrium T = T, where is defined as the ceiling temperature. At this temperature the rate of polymerization is equal to the rate of depolymerization. If the rate of reaction is considered to be the rate of loss of monomer, at the ceiling temperature the rate of polymerization is zero, as can be seen from Figure 1.23. 

These systems can be inside large halls and may have no fixed limits for their influence, except for some parts of the system (inlet device surface, etc.) They can also be situated inside small rooms, where walls, floors, and ceilings are the natural boundaries. The systems usually consist of one exhaust hood and one supply inlet, which interact. There are also special combinations, as two or more inlets and one exhaust hood, or one supply inlet and two or more exhausts. All of these combinations need careful design and an accurate relation between supply and exhaust flow rates and velocities. Some systems also need stable temperature conditions to function properly. All combinations are dependent on having a defined contaminant concentration in the inlet air. This usually implies clean supply air, but some systems may use recirculated air with or without cleaning. 

In thermal building simulation, a thermal zone can be a part of a room, a room, or a combination of rooms defined as a part of the conditioned space, throughout which the internal temperature is assumed to have negligible spatial variations. The zone is enclosed by the surrounding walls (floor, ceiling, roof, wall elements) and windows. 

With many monomers the equilibrium monomer concentrations at ambient temperatures are too small to be measiu-ed directly since the ceiling temperatimes are relatively high. However, they may be obtained via extrapolation (430). Some of the deviations from simple kinetic behavior at high temperatiu-es recorded in the older literature can be explained by the occurrence of depropagation. Use of the effective monomer concentration, defined as the total concentration minus the equiHbrilun concentration, removes the discrepancies. 

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