Temperature-time

Most response functions of poiymers obey a time-temperature or frequency-temperature superjDosition [43, 44], A change in temperature is equivaient to a shift of tire iogaritiimic frequency axis ... 

This experiment examines the effect of reaction time, temperature, and mole ratio of reactants on the synthetic yield of acetylferrocene by a Eriedel-Crafts acylation of ferrocene. A central composite experimental design is used to find the optimum conditions, but the experiment could be modified to use a factorial design. 

The preceding example of superpositioning is an illustration of the principle of time-temperature equivalency. We referred to this in the last chapter in connection with the mechanical behavior of polymer samples and shall take up the... 

The kinetic nature of the glass transition should be clear from the last chapter, where we first identified this transition by a change in the mechanical properties of a sample in very rapid deformations. In that chapter we concluded that molecular motion could simply not keep up with these high-frequency deformations. The complementarity between time and temperature enters the picture in this way. At lower temperatures the motion of molecules becomes more sluggish and equivalent effects on mechanical properties are produced by cooling as by frequency variations. We shall return to an examination of this time-temperature equivalency in Sec. 4.10. First, however, it will be profitable to consider the possibility of a thermodynamic description of the transition which occurs at Tg. 

The procedure described above is an application of the time-temperature correspondence principle. By shifting a set of plots of modulus (or compliance) versus time (or frequency) at any temperature (subscript 1) along the log t axis, we obtain the value of that mechanical property at another time and temperature (subscript 2). Using the shear modulus as an example, the time-temperature correspondence principle states... 

We shall presently examine the physical significance of the shift factors, since they quantitatively embody the time-temperature equivalence principle. For the present, however, we shall regard these as purely empirical parameters. The following Ust enumerates some pertinent properties of a ... 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

Variations in the Force Due to Gravity. The mass of an object is the quantity of matter ia the object. It is a fundamental quantity that is fixed, and does not change with time, temperature, location, etc. The standard for mass is a platinum—iridium cylinder, called the International Kilogram, maintained at the International Bureau of Weights and Measures, ia Snvres, France. The mass of this cylinder is 1 kg by definition (9). AH national mass standards are traceable to this artifact standard. 

The successflil appHcation of time—temperature superposition (159) for polystyrene foam is particularly significant in that it allows prediction of long-term behavior from short-term measurements. This is of interest in building and constmction appHcations. 

Vehicle Fa.ctors. Because knock is a chemical reaction, it is sensitive to temperature and reaction time. Temperature can in turn be affected either by external factors such as the wall temperature or by the amount of heat released in the combustion process itself, which is directiy related to the density of the fuel—air mixture. A vehicle factor which increases charge density, combustion chamber temperatures, or available reaction time promotes the tendency to knock. Engine operating and design factors which affect the tendency to produce knocking are... 

A molten metal alloy would normally be expected to crystallize into one or several phases. To form an amorphous, ie, glassy metal alloy from the Hquid state means that the crystallization step must be avoided during solidification. This can be understood by considering a time—temperature—transformation (TTT) diagram (Eig. 2). Nucleating phases require an iacubation time to assemble atoms through a statistical process iato the correct crystal stmcture... 

Fig. 2. Time—temperature—transformation (TTT) diagram where A represents the cooling curve necessary to bypass crystallization. The C-shaped curve separates the amorphous soHd region from the crystalline soHd region. Terms are defined ia text.

Alternative representations of stream temperature and energy have been proposed. Perhaps the best known is the heat-content diagram, which represents each stream as an area on a graph (3) where the vertical scale is temperature, and the horizontal is heat capacity times flow rate. Sometimes this latter quantity is called capacity rate. The stream area, ie, capacity rate times temperature change, represents the enthalpy change of the stream. 

K. C. Lee, J. L. Hansen, and D. C. Macauley, "Predictive Model of the Time-Temperature Requirements for Thermal Destmction of Dilute Organic Vapors," 72nd nnual 4PCA Meeting, Cincinnati, Ohio, June 1979. 

Eig. 15. Time—temperature transformation ia a thin-phase change layer during recording/reading/erasiug (3,105). C = Crystalline phase A = amorphous phase = melting temperature = glass-transition temperature RT = room temperature. 

Other conventions for treating equiUbrium exist and, in fact, a rigorous thermodynamic treatment differs in important ways. Eor reactions in the gas phase, partial pressures of components are related to molar concentrations, and an equilibrium constant i, expressed directiy in terms of pressures, is convenient. If the ideal gas law appHes, the partial pressure is related to the molar concentration by a factor of RT, the gas constant times temperature, raised to the power of the reaction coefficients. 

Pasteurization may be carried out by batch- or continuous-flow processes. In the batch process, each particle of milk must be heated to at least 63°C and held continuously at this temperature for at least 30 min. In the continuous process, milk is heated to at least 72°C for at least 15 s ia what is known as high temperature—short time (HTST) pasteurization, the primary method used for fluid milk. For milk products having a fat content above that of milk or that contain added sweeteners, 66°C is requited for the batch process and 75°C for the HTST process. For either method, foUowiag pasteurization the product should be cooled quickly to <7.2° C. Time—temperature relationships have been estabHshed for other products including ice cream mix, which is heated to 78°C for 15 s, and eggnog, which must be pasteurized at 69°C for 30 min or 80°C for 25 s. 

An airspace heater ejects steam into the airspace above the product and into the foam, maintaining a temperature at least 5°C above the minimum hoi ding temperature of 63°C. The time—temperature exposure is recorded on a chart which must be kept for proof of treatment. If the Hd is opened, and the milk temperature falls below 63°C, the exposure is intermpted causing the pasteurization cycle to restart. 

G. E. Vander Voort, ed.. Atlas of Time-Temperature Diagramsfor Irons and Steels, ASM International, 1991. 

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