Time-temperature transformation reaction

Figure 8.27 The thermosetting process as illustrating by the time-temperature-transformation reaction diagram (112).

For the tin pest reaction, the time exponent, n, is 3 [60]. Using the data in Ref. 52, it is approximated that a 40% volume fraction transforms after 1.5 years at —18°C, which yields a calculated value of K= 5.7 x lO sec when substituted into Eq. (2). It was also noted in Ref. 52 that tin pest was evident after 0.58 years. This results in approximately 2% of the volume transformed based on the previously calculated value of K. These time-temperature transformation reaction kinetics yield the classic S-shaped curves when the volume fraction transformed is plotted against the log of time. On that basis, it would require approximately 8.4x 10 min to transform 50% of a 99.5Sn-0.5Cu alloy. Other measurements of reaction kinetics in pure tin [56] are given in Table 6 which indicates that the time to transform a 50% volume fraction at — 15°C is 72 min. This difference, a factor of 10,000, is due to several parameters alloy additions, surface condition, residual stress, and prior thermal history. This very large difference in reaction rate illustrates the difficulty encountered when a tin-based solder is evaluated for use in microelectronic assemblies. Fig. 14 depicts the effect of temperature on the growth rate of the white-to-gray tin transformation. The maximum growth rate occurs at —40°C and decreases by a factor of 10 as the temperature approaches 0°C [56]. 

Construct a time-temperature-transformation diagram for a thermoset that follows a second order reaction kinetic model described by... 

Experimental time-temperature-transformation (TXT) diagram for Ti-Mo. Xhe start and finish times of the isothermal precipitation reaction vary with temperature as a result of the temperature dependence of the nucleation and growth processes. Precipitation is complete, at any temperature, when the equilibrium fraction of a is established in accordance with the lever rule. Xhe solid horizontal line represents the athermal (or nonthermally activated) martensitic transformation that occurs when the p phase is quenched. 

Gillham (107-112) pointed out the need to postcure the polymer above T oo, the glass transition temperature of the fully cured system. He developed a time-temperature-transformation (TTT) reaction diagram that may be used... 

Time-temperature-transformation curve forTi-51 Ni, which shows precipitation reactions as a function of temperature and time. Source M. Nishida, C.M. Wayman, and T. Honma, Melall. Trans. A Vol 17,1986, p 15(B... 

Several constraints are imposed on the use of diagrams like Figure 10.13. First, this particular plot is valid only for an iron-carbon alloy of eutectoid composition for other compositions, the curves have different configurations. In addition, these plots are accurate only for transformations in which the temperature of the alloy is held constant throughout the duration of the reaction. Conditions of constant temperature are termed isothermal thus, plots such as Figure 10.13 are referred to as isothermal transformation diagrams or sometimes as time-temperature-transformation (or T-T-T) plots. 

Depending on the reaction temperature and reaction time, tetrahydroisoquinoline 357 afforded different mixtures of 1,2,3,4,11,11 a-hcxahydro-6//-pyrazino[ 1,2-3]isoquinolines 358-361 and tetracyclic compound 362 (Scheme 30) <2005JA16796>. Each of the individual diastereoisomers 358-361 could be transformed into the compound 362. z7r-3//,4a//-3-Phcnylpcrhydropyra/ino[ 1,2-7]isoquinoline-l,4-dione was prepared via automated parallel solid-phase synthesis on Kaiser oxime resin <1998BML2369>. l,2,3,5,6,7-Hexahydropyrido[l,2,3-r/f ]quinoxaline-2,5-dionc was obtained by catalytic hydrogenation of ethyl 3-(2-oxo-l,2,3,4-tetrahydro-5-quinoxalinyl)acrylate in the presence of TsOH over 5% Pd/C catalyst under 40 psi of hydrogen <1996JME4654>. 

Reaction-based indicators which are catalytically transformed by the analyte of interest are an attractive alternative due to the simple reason mentioned in the context of enzymes at the beginning of Sect. 4 one analyte molecule is qualified to produce a lot of fluorophores, increasing sensitivity dramatically. For an actual quantitative determination, however, the same conditional constraints are relevant like in enzyme-based methods, i.e., reproducible and defined incubation times, temperature, pH, etc. Up to now, transition metal cations have been mostly shown to be detectable by catalytic fluorophore production. 

Iron oxides present in coal are generally stable for the relatively short period of time that they are exposed to combustion temperatures. Therefore, siderophile elements (e.g., Ni, Co, Mo, Pt, Pd, Au) that are incorporated within iron oxides are also expected to remain stable, and escape any significant thermal transformation reactions (Bums 2003). Similarly, lithophile elements (e.g., Ba, B, Cr, Mn, Sr, V) that are initially found in association with silicates and aluminosilicates in coal are expected to be incorporated within the glassy fraction of coal ash upon thermal transformation of their parent minerals (Bums 2003). 

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