Characteristic temperature point

Another characteristic temperature point is the intersection of lightness (L ) hysteresis curves for the heating and the cooling cycle. The temperature can be determined with 100% accuracy at the point of intersection without the need of knowing which of the two cycles led to the particular level of lightness (L ). 

Fig. 6.5 (a) Temperature dependence of the order parametru in the Landau-de Gennes model (B) and (C) are coefficients of the expansion. Tjvj Tc is experimental value of the isotropic—nematic phase transition temperature corresponding to equality of free energy densities for the two phases, (b) Experimental dependence of the order parameter for 5CB and the characteristic temperature points Tc, Tc and Tc defined in accordance with the model of panel (a)... 

Of all the characteristic points in the phase diagram, the composition of the middle phase is most sensitive to temperature. Point M moves in an arc between the composition of the bottom phase (point B) at and the composition of the top phase (point T) at reaching its maximum surfactant concentration near T = - -T )/2. (Points B and Tmove by much smaller amounts, also.) The complete nonionic-amphiphile—oh—water—temperature... 

The burden must have a definite sohdification temperature to assure proper pickup from the feed pan. This limitation can be overcome by side feeding through an auxiliary rotating spreader roll. Apphcation hmits are further extended by special feed devices for burdens having oxidation-sensitive and/or supercoohng characteristics. The standard double-drum model turns downward, with adjustable roll spacing to control sheet thickness. The newer twin-drum model (Fig. ll-55b) turns upward and, though subject to variable cake thickness, handles viscous and indefinite solidification-temperature-point burden materials well. 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

On the other hand, it is clear that in the classical regime, T> (T i is the crossover temperature for stepwise transfer), the transition should be step-wise and occur through one of the saddle points. Therefore, there should exist another characteristic temperature. r 2> above which there exist two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points atlT = T i. The existence of the second crossover temperature, 7, 2, for two-proton transfer has been noted by Dakhnovskii and Semenov [1989]. 

Boiling Point at 1 atm - Defined as the characteristic temperature of a liquid when its vapor pressure is 1 atm. As an example, when water is heated to 100°C (212°F), its vapor pressure rises to 1 atm and the liquid boils. The boiling point at 1 atm indicates whether the liquid will boil and become a gas at any particular temperature and at sea-level atmospheric pressure. 

Zone temperature control characteristics (set point, type of thermostat, throttling range)... 

Mention of the approach given by van Krevelen et al. [529,530] has already been made. Other methods based on points of inflection have been described but in some treatments it would seem probable that the integration constant has been omitted [559]. Doyle s treatment [533] avoids this error by using a characteristic temperature, 0 = T— Tm, where Tm is the temperature at which the reaction rate reaches a maximum. Doyle writes... 

Fig. 1. Schematic one-dimensional cross section through the Gibbs free energy surface G(R) of a spin-state transition system along the totally symmetric stretching coordinate. The situation for three characteristic temperatures is shown (B = barrier height, ZPE = zero-point energy, 28 = asymmetry parameter, J = electronic coupling parameter, AG° = Gh — GJ...

Surfactant blends of interest will exhibit clouding phenomena in aqueous solutions undergoing a phase transition from a one phase system to a two phase system at a discrete and characteristic temperature, referred to as the Cloud Point (CP). This value indicates the temperature at which sufficient dehydration of the oxyethylene portion of the surfactant molecule has occurred and this results in its "displacement" from solution. The addition of lyotropic salts will depress the CP, presumably due to the promotion of localised ordering of water molecules near the hydrophilic sheath of the surfactant molecule (8). Furthermore, the addition of different oils to surfactant solutions can induce either an elevation or a depression of the recorded CP and can be used to qualitatively predict the PIT (8x9). 

However, the characteristics of point b with regard to temperature fluctuations are quite different. At this point the slope of the energy release curve is greater than the slope of the energy loss curve. If a small positive temperature fluctuation were to occur, one would be in a... 

However, for most studies, DTA has been mostly used in a qualitative sense as a means to determine the characteristic temperatures of thermally induced reactions. Owing to the experimental conditions used for its measurement, the technique is most useful for the characterization of materials that evolve corrosive gases during the heating process. The technique has been found to be highly useful as a means for compound identification based on the melting point considerations, and has been successfully used in the study of mixtures. 

The boiling points of different types of liquids vary widely. They are an important physical characteristic both of liquids and of the many solids that melt to become liquids and then boil at a certain characteristic temperature. 

Monomer and initiator must be soluble in the liquid and the solvent must have the desired chain-transfer characteristics, boiling point (above the temperature necessary to carry out the polymerization and low enough to allow for ready removal if the polymer is recovered by solvent evaporation). The presence of the solvent assists in heat removal and control (as it also does for suspension and emulsion polymerization systems). Polymer yield per reaction volume is lower than for bulk reactions. Also, solvent recovery and removal (from the polymer) is necessary. Many free radical and ionic polymerizations are carried out utilizing solution polymerization including water-soluble polymers prepared in aqueous solution (namely poly(acrylic acid), polyacrylamide, and poly(A-vinylpyrrolidinone). Polystyrene, poly(methyl methacrylate), poly(vinyl chloride), and polybutadiene are prepared from organic solution polymerizations. 

Figure 13. Ratios T/ /To and Ti/Tg of the characteristic temperatures from Figs. 8a and 8b as a function of the inverse number l/M oi united atom groups in individual chains for constant pressure (P = 1 atm 0.101325 MPa)F-F (open symbols) and F-S (filled symbols) polymer fluids. The single data point denoted by refers to high molar mass F-S polymer fluid at a pressure of P = 240 atm (24.3 MPa).

At the surface of a liquid, molecules can enter the gas phase more easily than elsewhere within the liquid because the motions of those molecules ciren t as constrained by the molecules around them. So these surface molecules can enter the gas phase at temperatures below the liquid s characteristic boiling point. This low-temperature phase change is called evaporation and is very sensitive to pressure. Low pressures allow for greater evaporation, while high pressures encourage molecules to re-enter the liquid phase in a process called condensation. 

Vanadium oxytrichloride is a lemon-yellow liquid. Its boiling point is 124.5°C. at 736 mm. and 127.16°C. at 760 mm. It remains liquid at —77°. The vapor pressure at —77° is 4.1 mm. at 0°, 21 mm. and at 85°C., 270 mm. Its density in grams per milliliter is 1.854 at 0° and 1.811 at 32°C. At ordinary temperatures, it neither dissolves nor reacts with carbon, hydrogen, nitrogen, oxygen, silicon, tellurium, or metals except the alkali metals and antimony. The reactions with the alkali metals are explosive at characteristic temperatures, varying from 30°C. for cesium to 180°C. for sodium (lithium not determined). Small... 

The potential (6.37) corresponds with the previously discussed projection of the three-dimensional PES V(p,p2,p3) onto the proton coordinate plane (pi,p3), shown in Figure 6.20b. As pointed out by Miller [1983], the bifurcation of reaction path and resulting existence of more than one transition state is a rather common event. This implies that at least one transverse vibration, q in the case at hand, turns into a double-well potential. The instanton analysis of the PES (6.37) was carried out by Benderskii et al. [1991b], The existence of the onedimensional optimum trajectory with q = 0, corresponding to the concerted transfer, is evident. On the other hand, it is clear that in the classical regime, T > Tcl (Tc] is the crossover temperature for stepwise transfer), the transition should be stepwise and occur through one of the saddle points. Therefore, there may exist another characteristic temperature, Tc2, above which there exists two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points at T = Tcl. The existence of the second crossover temperature Tc2 for two-proton transfer was noted by Dakhnovskii and Semenov [1989]. 

The dielectric properties of oligodimethylsiloxanes and their dependence on temperature point to good dielectric characteristics of PMS liquids. Taking into consideration that PMS do not form conductive carbon particles in case of electric breakdown or sparking, it is obvious why they are used as liquid dielectrics in transformers and other electric devices. There is a law in Japan and the USA which forbids the use of nonflammable yet toxic pentachlorodiphenyl and leaves room for oligodimethylsiloxanes. This has stimulated a much more active production of PMS liquids in Japan, Germany and other countries. 

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