Relaxation enthalpy

TNM expression for enthalpy relaxation is a result of introducing 7/ into Arrhenius equation for rand is given by. 

The parameters of the TNM and AGV equations can be compared and the constants may be related as follows. 

A// near Tg and also small values of AQ, whereas in fragile liquids these quantities have large values. 

The glassy state of materials prepared under normal conditions is in a non-equilibrium state, in which an excess volume and enthalpy exist. When such a non-equlibrium glassy state is held at temperatures a few degrees lower than T, the excess thermodynamic properties decrease to those of an ideally equilibrium state. At the same time, the mechanical properties of the materials change (lOj. 

For a quenched glass, only a step in the heat capacity is observed at T. For an aimealed glass, however, not only a step but also a peak of heat capacity, which corresponds to the rapid recovery of the enthalpy, are observed at T. On annealing, the area of the endothermic peak 

The following equation can be used in order to compare the relaxation times of polymer glasses  

From equation (4.7), the relaxation time, r is obtained as follows  

The relaxation time, r, -2 for which the enthalpy is reduced to half of the initial excess enthalpy, shows an Arrhenius temperature dependence, expressed as 

Schematic diagram of the change of V, H, S, and the derivatives Cp and oc with temperature on slow cooling, followed by fast heating. The shaded areas must be equal.  

The sample is then cooled at a rate q, to the annealing temperature (point B) in the glass. The rate q must be controlled and be the same for all the measurements, if results are to be consistent, as the distance of the sample from its equilibrium state at Ta depends on the rate at which the material is cooled. The sample is then held at for a specified time during which physical aging occurs, as seen by the loss of 

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Chung, H.-J., Lee, E.-J., and Lim, S.-T. (2002). Comparison in glass transition and enthalpy relaxation between native and gelatinized rice starches. Carbohydr. Polym. 48, 287-298. 

Chung, H. -J., Woo, K. -S., Lim, S. -T. (2004). Glass transition and enthalpy relaxation of eross-linked corn starches. Carbohydr. Polym., 55, 9-15. 

Enthalpy relaxation is often responsible for two endothermic transitions in the initial dsc thermograms, and a single, broad transition is observed in most second scans and in dmta thermograms. 

Hodge, I. M., and Huvard, G. S. (1983). Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 3. Experimental and modeling studies of polystyrene. Macromolecules 16(3), 371-375. 

Privalko, V. P, Demchenko, S. S., and Lipatov, Y. S. (1986). Structure-dependent enthalpy relaxation at the glass transition of polystyrenes. Macromolecules 19(3), 901-904. 

DSC was utilized to study both the state of the cure (extent of crosslinking) and the kinetics of enthalpy relaxation in crosslinked epoxies >8.21.56.71,72) results... 

DSC has been amply demonstrated in the pat to be a useful instrument to follow the kinetics of enthalpy relaxation in polymers 41,42,74>. Figure 21 shows the DSC... 

Fig. 21. Influence of physical aging on the endothermic enthalpy relaxation of Fiberite 934 resin...

Fig. 22. Effect of reaging on the enthalpy relaxation of requenched Fiberite 934 resin...

The enthalpy relaxation peak appears near the onset of the transition from the glassy state to the rubbery state. This peak appears after only 10 minutes of aging. 

Enthalpy relaxation studies were carried out at 3 different temperatures 80, 110, and 140 °C. Compared to the 140 °C enthalpy relaxation data, the 110 °C aging... 

As mentioned earlier, the relaxation enthalpy was measured by superimposing the first and the second DSC scans for each specimen. Figure 23 shows the relaxation-enthalpy loss versus logarithmic sub-Tg annealing time at 80°, 110°, and 140 °C. There is clearly a linear relationship between the enthalpy relaxation process and the logarithmic aging time, Ta. 

A melted sample of the terpolymer was cooled in the calorimeter at 320°/min to — 40°C and was allowed to remain at — 40°C for 16 hr after which the temperature was lowered to — 150°C. Upon reheating, the Tg of the annealed sample increased to — 31 °C moreover, an additional adsorption of thermal energy was superimposed upon the normal increase in Cp during the glass transition. The additional increase in enthalpy, 0.5 cal/g, is the result of enthalpy relaxation occurring during... 

Very important phenomena in polymer behaviour, such as viscoelasticity, stress, strain, volume and enthalpy relaxation, ageing, etc., are characterised by time-dependence of the polymer properties. 

Table 12.3. Glass transition temperatures Tg and the activation energies AFreiax of enthalpy relaxation of dry amorphous disaccharidesa...

As shown in Table 12.3, dry trehalose vitrifies at a higher temperature than do other disaccharides and the resultant glassy matrix is highly stable in the sense that enthalpy relaxation occurs with more difficulty than in other... 

Haida O, Matsuo T, Suga H, Seki S (1974) Calorimetric study of the glassy state, X. Enthalpy relaxation at the glass transition temperature of hexagonal ice. J Chem Thermodyn 6 815-825... 

The effect of the type of impact modifier on the melt flow of a PVC window profile formulation as a function of shear rates encountered during extrusion was investigated and the relationship between the melt flow and mechanical properties of the profiles evaluated. A Rheoplast Capillary Rheometer with a pre-shearing device was employed to investigate the melt viscoelastic properties of the formulations and the performance of the formulations in terms of post-extrusion shrinkage, surface gloss and enthalpy relaxation discussed. 2 refs. 

In conclusion, the deformation behavior of poly(hexamethylene sebacate), HMS, can be altered from ductile to brittle by variation of crystallization conditions without significant variation of percent crystallinity. Banded and nonbanded spherulitic morphology samples crystallized at 52°C and 60°C fail at a strain of 0.01 in./in. whereas ice-water-quenched HMS does not fail at a strain of 1.40 in./in. The change in deformation behavior is attributed primarily to an increased population of tie molecules and/or tie fibrils with decreasing crystallization temperature which is related to variation of lamellar and spherulitic dimensions. This ductile-brittle transformation is not caused by volume or enthalpy relaxation as reported for glassy amorphous polymers. Nor is a series of molecular weights, temperatures, strain rates, etc. required to observe this transition. Also, the quenched HMS is transformed from the normal creamy white opaque appearance of HMS to a translucent appearance after deformation. 

This kind of non-exponential enthalpy relaxation can be found likely in some of the orientationally disordered crystals in their undercooled states, as exemplified typically by isocyanocyclohexane. In the room temperature phase, each isocyanocyclohexane molecule reorients rapidly along several unique axes in an fee unit cell, resulting in time- and space-averaged spherical symmetry of the molecule. The cubic phase is easily undercooled by avoiding the transformation into a low-temperature ordered phase. Finally the orientational... 

Among various techniques in producing non-crystalline solids, the vapor condensation is the most powerful method in extracting rapidly the energies of disordered system to form non-crystalline solids with extremely high ilctive temperatures. The enthalpy relaxation starts to occur at temperatures far below Tg. The relaxation rate can be described likely by the KWW empiric equation, as in the cases of many liquids with moderate departure from the equilibrium state. 

Structural relaxation times determined from enthalpy relaxation studies with sucrose and trehalose [37,50] are given in Figure 8. The structural relaxation times observed are qualitatively similar to those estimated for the fragile glass... 

Figure 8 Structural relaxation times for quench-cooled glassy disaccharides as determined from enthalpy relaxation data. Structural relaxation times were obtained by a fit of the data to the stretched exponential function (see [37,50]). ( ) Data for sucrose obtained by differential scanning calorimetry on annealed samples [37], (O) Data for sucrose obtained by isothermal microcalorimetry [50]. (A) Data for trehalose obtained by isothermal microcalorimetry [50].

The problems associated with freeze drying of peptides and proteins for therapeutic use have also received calorimetric attention recently - particularly, attempts to understand and interpret the dynamics of amorphous solids. Structural relaxation time is a measure of molecular mobility involved in enthalpy relaxation and thus is a measure of the dynamics of amorphous (glassy) solids. These dynamics are important in interpretation of the physicochemical properties and reactivities of drugs in amorphous formulations. The authors conclude that microcalorimetry may provide data useful for rational development of stable peptide and protein formulations and for control of their processing . 

Twin models. Figure 2 illustrates the temperature dependence of heat capacity for the two twin models and Table I gives the corresponding numerical data. Figure 2 typifies the Cp(T) curve of conventional glasses with a well defined enthalpy relaxation peak and smooth solid and liquid lines. From the extrapolated solid and liquid lines we can measure the heat capacity jump at Tg, by equation 1. Within our experimental range, the data fit a straight line with slopes (B) as listed in Table n. 

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