Other Fragility Measures

Overall, the results presented in Figs. 2.5 and 2.6 indicate that three independent measures of fragility can be obtained from simple DSC analysis of glass-forming materials. These methods specifically 

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An estimated 75 million people are affected by osteoporosis to some degree in the United States, Europe, and Japan. Osteoporosis is a systematic skeletal disease characterized by bone mass and microarchitectural deterioration with a consequent increase in bone fragility and susceptibility to fracture. Operationally, osteoporosis can be defined as a certain level of bone mineral density. The definition of osteoporosis is somewhat arbitrary and is based on epidemiological data relating fracture incidence to bone mass. Uncertainty also is introduced due to variability in bone densitometry measurements. Other clinical measures to assess the skeleton include collagen cross-links (measure of bone resorption) and levels of bone-specific alkaline phosphatase and osteocalcin (bone formation). A list of biochemical markers of bone remodeling is provided in Table 37-3. Measurement of total serum alkaline phosphatase level and urinary hydroxyproline or calcium levels is of limited value. 

Vulnerability is not fragility. Vulnerability measures loss fragility measures probability. Vulnerability functions are referred to many ways damage functions, loss functions, vulnerability curves, and probably others. 

In an acid-base titration, you carefully measure the volumes of acid and base that react. Then, knowing the concentration of either the acid or the base, and the stoichiometric relationship between them, you calculate the concentration of the other reactant. The equivalence point in the titration occurs when just enough acid and base have been mixed for a complete reaction to occur, with no excess of either reactant. As you learned in Chapter 8, you can find the equivalence point from a graph that shows pH versus volume of one solution added to the other solution. To determine the equivalence point experimentally, you need to measure the pH. Because pH meters are expensive, and the glass electrodes are fragile, titrations are often performed using an acid-base indicator. 

Volume swelling measurements have produced erratic results even under the most carefully controlled conditions. One important contribution in this regard is the work of Bills and Salcedo (8). These investigations showed that the binder-filler bond could be completely released with certain solvent systems and that the volume swelling ratio is independent of the filler content when complete release is achieved. Some thermodynamic problems exist, however, when such techniques are used to measure crosslink density quantitatively. First, equilibrium swelling is difficult to achieve since the fragile swollen gel tends to deteriorate with time even under the best conditions. Second, the solubility of the filler (ammonium perchlorate) and other additives tends to alter the solution thermodynamics of the system in an uncontrollable manner. Nonreproducible polymer-solvent interaction results, and replicate value of crosslink density are not obtained. 

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