Ceiling floor temperature

Equations (1) and (2) indicate that AH and AS must both be either positive or negative 

The equilibrum constant K of eqn. (2) is given by the ratio of the propagation and depropagation rate constants, 

The temperature derivative of the logarithmic form of eqn. (4) yields the temperature dependence of the equilibrium constant (Van t Hoff isobarf 

The concept of the limiting polymerization temperature has been elaborated by Dainton and Ivin l Originally they only considered T, and they took the name from previous studies [2] ceilling temperature T . In the literature it is still usually designated by this symbol. Eisenberg and Tobolsky [3] are the authors of the broader concept of polymerization equilibria. Due to fluctuations in monomer addition, both and vary, and is statistical in character. It is rather a temperature interval of some width. Sometimes it is defined as the temperature above which the formation of a high polymer P 100) is excluded  

For a given monomer, and Tj-depend on the initial and final states. This follows from eqn. (3). The value of AS is not constant for all cases, of course. It depends on the size of the various entropy contribution. Evidently it is always necessary to characterize the initial and final states in order to prevent misunderstanding. 

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This concept of ceiling/floor temperature formulated for homopolymerization can be applied to copolymerization as well. Similarly as for homopolymerization, the ceiling temperature can be found in these copolymerization systems in which, while increasing the temperature, we get positive A yG and consequently the depolymerization of a copolymer (provided the active species of the copolymerization are alive). On the other hand, when spontaneous depolymerization occurs... 

Equilibrium Monomer Concentration Ceiling/Floor Temperatures... 

Characteristics of the air jet in the room might be influenced by reverse flows, created by the jet entraining the ambient air. This air jet is called a confined jet. If the temperature of the supplied air is equal to the temperature of the ambient room air, the jet is an isothermal jet. A jet with an initial temperature different from the temperature of the ambient air is called a nonisother-mal jet. The air temperature differential between supplied and ambient room air generates buoyancy forces in the jet, affecting the trajectory of the jet, the location at which the jet attaches and separates from the ceiling/floor, and the throw of the jet. The significance of these effects depends on the relative strength of the thermal buoyancy and inertial forces (characterized by the Archimedes number). 

In displacement ventilation systems air is supplied to the room at low velocity, with a volume flow rate near the floor, and is extracted near the ceiling. The temperature of the supplied air is slightly lower than that of the room. Air is heated by the objects in the room, e.g., computer terminals and photocopying machines, and it rises due to buoyancy. 

The ceiling temperature phenomenon is observed because AH is highly exothermic, while AS is mildly exoentropic. The opposite type of phenomenon occurs in rare instances where AS is endoentropic (AS = +) and AH is very small (either + or —) or zero. Under these conditions, there will be a floor temperature Tf below which polymerization is not possible. This behavior has been observed in only three cases—the polymerizations of cyclic sulfur and selenium octamers and octamethylcyclotetrasiloxane to the corresponding linear polymers (Secs. 7-lla). AH is 9.5, 13.5, and 6.4 kJ mol-1, respectively, and AS is 27, 31, and 190 J K-1 mol-1, respectively [Brandrup et al., 1999 Lee and Johannson, 1966, 1976]. 

Part V Properties determining the chemical stability and breakdown of polymers. In Chapter 20, on thermomechanical properties, some thermodynamics of the reaction from monomer to polymer are added, included the ceiling and floor temperatures of polymerization. Chapters 21 and 22, on thermal decomposition and chemical degradation, respectively, needed only slight extensions. 

The indicated procedure for analyzing the kinetics of non-stationary polymerizations is evidently unacceptably simplified, and may serve only as a very rough model for the analysis of actual situations. An exact general procedure should include thermodynamic principles (floor and ceiling polymerization temperatures), detailed concepts on the generation and decay of active centres and on transfer (especially degradative). 

In exoenthalpic and exoentropic polymerizations, AGP° eventually becomes positive above a temperature known as the ceiling temperature (AGP° = AHP°/TCASP° > 0). For example, the ceiling temperature of bulk styrene is =400° C, whereas that of methyl methacrylate is =200° C. In contrast, AGP° becomes positive below a floor temperature when the polymerization is endoenthalpic and endoentropic (AGP° = AHp°/TfASp° > 0), such as in the polymerization of Sg (T/ = 160° C). 

The ceiling (or floor) temperature varies with the equilibrium monomer concentration, with the highest (or lowest) temperature corresponding to that of a bulk polymerization [Eq. (18)]. 

The terms ceiling and floor temperatures usually refer to bulk conditions unless stated otherwise. Because polymerization does not occur when the initial monomer concentration is at or below the equilibrium monomer concentration, [ML in the above equations can be replaced with [M]0. This demonstrates that AGP will be negative even if AGP° is positive if [M]0 is high enough, and that polymerization will occur. For example, although tetrahydrofuran (THF) does not polymerize at 25° C when [M]0 = 1 mol/L (4 Gp° > 0), it does polymerize at concentrations [M]0 > 5 mol/L (AGP < 0) because at 25° C [ML 5 mol/L [29]. 

These interactions are much less pronounced in the polymer and the resulting gain in internal rotational entropy provides a driving force for the polymerization. Thus, by increasing the size of substituents one may pass from a system for which AH and AS° are both negative and which exhibits a ceiling temperature, to a system with positive AH and AS characterized by a floor temperature. 

Second, by more rapid crosspropagation than homopropagation. This happens when the more reactive monomer cannot homopolymerize due to unfavorable thermodynamics e.g. the system being above the ceiling or below the floor temperature. 

Most monomers exhibit an exothermic polymerization reaction (negative and large AH) with a small but negative entropy change. In that case, they have a ceiling temperature as described in the previous section. However, a few exceptional monomers (e.g., cyclic sulfur) exhibit a very small AH (either positive or negative) with a positive entropy change. In these cases, the polymerization will have a floor temperature below which the polymerization does not proceed. 

Natural fiber (jute fabric) and industrial wastes are used along with polymer to make composite wood substitute products. In this process, processed fabric of jute fiber and industrial wastes such as fly ash/red mud/marble sluny dust with polymer were synthesized in molds of required length and width. The composite laminates were fabricated with requisite pressure and cured at room temperature. Various products such as full size door shutters and panels can be fabricated and designed according to requirement. The industrial waste-based polymer composite products are comparable to natural wood and thus could be used as a wood substitute for doors, windows, ceilings, flooring, partitions, and furniture, etc. The products are cost-effective and no further maintenance is required. This is an environment friendly product with fruitful utilization of fly ash/red mud/marble slurry dust (Table 22.14). The salient features of the products are ... 

In some special cases, however, the pol5mierization is an endothermic reaction (positive AiT) compensated by an increase in entropy. Such a case is the polymerization of elemental, eight-membered, cyclic sulfur, Ss (147). It follows that, in such a polymerization, a minimum temperature exists below which polymerization is not possible and an inverse ceiling temperature, a floor temperature, exists. This situation can also occur in ring-opening pol5mierizations, where a priori predictions of the signs in AS and AiT are not possible (148). 

What does it mean when a polymer has both a floor temperature and a ceiling temperature ... 

Thermodynamics of reversible homopolymerization and copolymerization are revisited. The equilibrium rate constant is expressed as a function of free energy. Methods to calculate the ceiling and floor temperature are outlined. 

When the forward and reverse reactions have equal rates, namely when polymerization-depolymerization propagation rates are equal, the concept of ceiling and floor temperatures arises. Most polymerizations have ceiling temperatures, temperatures above which the monomer cannot be polymerized, but the polymer will spontaneously depolymerize back to the monomer. Commercially this fact leads to an important method of polymer recycling whereby scrapped polymer is heated under anaerobic conditions to allow distilling off the resultant monomers. 

Ceiling temperatures Tc and floor temperatures Tf of polymerizations in bulk are usually reported for Ai G or Aic-G for polymerizations of liquid monomers (subscript 1) to amorphous (subscript c) or crystalline (subscript c ) pol)mers. Polymerization in solution is usually referred to as the polymerization of a 1 moir monomer solution (subscript s) to a dissolved polymer (subscript s), that is, AssG° = 0. Ceiling temperatures in bulk (Tc(bulk)) are always higher than ceiling temperatures in solution. 

Analyzing thermodynamics of homopolymerization, the monomer polymerizability feature called the ceiling (or floor) temperature is often determined. 

Both terms describe the temperature at which a monomer and a polymer of a high molar mass and negligible quantity coexist at equilibrium and the difference between the ceiling and the floor temperature lies in what is below and above. 

Because of the dependence of A S on the monomer concentration, the ceiling and floor temperatures are dependent on the monomer concentration in feed. 

From thermodynamies, we know that a proeess oceurs spontaneously only when AGp is negative and, at equilibrium, AGp is zero. In ease 1, AGp would be negative below a eertain temperature and positive above it. This implies that the reaction would occur only below this temperature, which is called the ceiling temperature. In case 2, AGp is always negative and, therefore, the polymerization occurs at all temperatures. In case 3, AGp is always positive and therefore the reaction does not go in the forward direction. In case 4, the reaction would occur only when the temperature of the reaction is above a certain value, called the floor temperature. 

Values of thermodynamic parameters characterizing the polymerization ability of the most important cyclic and heterocycUc monomers are compared in Table 1.1. Equation 1.6 indicates that, at standard conditions, monomers for which AHp < 0 and ASp > 0 can be polymerized at any temperature, whereas those with AHp > 0 and ASp < 0 cannot be converted into Unear macromolecules. In the most typical case-that is, when AHp < 0 and AS[] < 0-an increase in the polymerization temperature leads to an increase in [M]eq (Equation 1.7b). Eventually, at or above the so-called ceiling temperature (T Equation 1.9a), at which [M]eq = [M]o, formation of the high polymer does not occur. In contrast, for AHp > 0 and ASp > 0, [Mje, decreases with increasing temperature (Equation 1.7b) and there is another critical temperature-called the floor temperature (Tf, Equation 1.9b), at or below which polymerization is thermodynamicaUy forbidden. 

Wood in its untreated form has good resistance or endurance to fire penetration when used in thick sections for walls, doors, floors, ceilings, beams, and roofs. This endurance is due to low thermal conductivity, which reduces the rate at which heat is transmitted to the interior. Typically, when the fire temperature at the surface of softwood is 870—980°C, the inner char 2one temperature is - 290° C, and 6 mm further inward, the temperature is 180°C or less. The penetration rate of this char line is mm/min, depending on the species, moisture content, and density (45,46). Owing to this slow... 

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