Glass transition fictive temperature

Temperature(s). See also Blackbody temperature sensor Cure temperature Curie temperature Eutectic temperature Fictive temperature Furnace temperature Glass- transition temperatures Heat entries Heating Hot entries Refrigeration Target temperature emperature measurement Thermal entries Thermo-entries Transition temperatures in analysis of water, 26 35 biofiltration system, 10 76 in biological wastewater treatment,... 

Glass transition temperature or the fictive temperature may be investigated or diagrammed using different methods, resulting in different definitions. These... 

Enthalpy relaxation is one of the most widely studied in the context of both non-linearity and non-exponentiality of the measured glass properties. A convenient technique for these studies is scanning calorimetry. In simple cooling and heating experiments, heat capacity curves exhibit normal increase with characteristic hump of Cp above the glass transition as represented in Figure 9.08(A). The fictive temperature,... 

The time dependence of some thermodynamic properties of amorphous materials below the glass transition is shown in Figure 4. The actual position of Tg depends on the cooling rate. For many practical purposes, energies and densities, along with most other properties of vitrified materials, are expressed in terms of their relaxation times. A fictive temperature Jf (T,/), is introduced, which represents the temperature at which the quasi-equilibrium enthalpy of the undercooled liquid equals that of the non-equilibrium glass Tf T,t) then accounts for the temperature and time dependence of the non-equilibrium state. The significance and usefulness of the fictive temperature is discussed in Chapter 11. 

A fictive temperature 7 based approach firstly introduced by Tool [47] has been proved to be extremely successful in supplying the information about the free volume or the structure in the formulation of the free energy density. The fictive temperature 7/ is an internal variable to characterize the actual thermodynamic state during the glass transition, defined as the temperature at which the temporary nonequilibrium stmcture at T is in equilibrium [20]. It was assumed that the rate change of the fictive temperature is proportional to its deviation from the actual temperature and the proportionality factor depends on both T and Tf [48], as indicated in the evolution equation [47] ... 

The Fictive Temperature and Enthalpy Loss on Annealing The fictive temperature (Tgf) can be obtained by extrapolation of the linear portions of the enthalpy lines above and below the glass transition as illustrated in Figure 1.18. This can be calculated in the case of MTDSC from the following approximate relationship. 

The kinetic nature of the experimentally observed glass transition (at Tg) is ever present. For any reasonable cooling rate, a temperature will always be reached where equilibrium cannot be maintained and the properties of the solid (including specific volume and configuration entropy) will be determined by its thermal history. This kinetic nature of the glass transition led to the concept of the fictive temperature, as the temperature at which the glass would be in thermodynamic equilibrium (Tool (1964)). The fictive temperature of a material thus depends upon each sample s thermal history. 

The absolute need for a distribution of relaxation times can be illustrated by a more complicated thermal history. The sample is annealed to equilibrium above the glass-transition interval and then quenched rapidly to a temperature deep within the glass-transition region. It is isothermally annealed until its volume achieves a value consistent with a glass with a fictive temperature in the middle of the glass-transition interval. The partially annealed glass is then rapidly heated to this fictive temperature, where the sample achieves a volume exactly equal to its equilibrium value. The volume then increases spontaneously to a maximum value and finally relaxes back to its equilibrium volume. This trajectory is called the "memory effect" and is shown in Figure 8.2. 

Figure 6.26 Determination of the (fictive) glass transition temperature. Solid lines are from measured data of a glass transition with enthalpy relaxation dotted lines are linearly extrapolated. The glass transition temperature is thermodynamically defined...

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