State diagrams

The Cg value, the concentration of the maximally freeze concentrated glass (see Glossary), for most carbohydrate solutions has a similar value (see Table 9.3). Highly viscous solutions do not reach equilibrium, and a cooling curve will follow the lower trajectory on graph 1.14 (see Chapter 1). This means that the concentration of water in the glass is actually above the equilibrium content, and subsequent heating will increase mobility such that the excess water can recrystallise to form ice. Both Tg and Cg will thus be difficult to obtain from simple measurements. 

The meaning of the features observed on DSC traces of frozen carbohydrate (malto-oligomers and sucrose) solutions has been clarified by the work of Ablett etal. [137, 138]. 

This work explained discrepancies, such as the apparent variations in Cg as a function of the sucrose concentration. It was shown that the main sources of error were the assumptions of a temperature-independent latent heat of fusion of ice and a linear background for calculation of the enthalpy and hence ice content. Moreover, an error analysis of the 

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Fig. 7. Phase or state diagram for horizontal conveying where represents a particular mass flow rate, line AB corresponds to the pressure drop for air alone flowing in the system, Gq = 0, and ( is the minimum pressure line where saturation occurs. Other points ate explained in text.

One widely-used picture for illustrating the different types of flow in pneumatic conveying is the so-called state diagram, - in which the pressure drop is related to the air velocity. 

Figure 12.16 Oxidation state diagram for phosphorus. (Note that all the oxoacids have a phosphorus covalency of 5.)...

Figure 13.16 Oxidation state diagram for As, Sb and Bi in acid and alkaline solutions, together with selected data on N and P for comparison.

Disproportionation of X2 in hot alkaline solution has long been used to synthesize chlorates and bromates (see oxidation state diagrams, p. 855) ... 

It is desirable and perhaps necessary to make the conditions, (21) and (23), explicit, since substitution of the equilibrium condition (12) into either (18) or (19), separately, gives results that makes this derivation appear suspect. The derivation is, however, valid, and it corresponds to a transition-state diagram containing three peaks. The last and highest one, which is lowered as the concentration of base increases, corresponds to the conversion of IV to product the first... 

The Ak values in x-, y- and z-direction are properly separated from each other and only discrete energy levels are allowed (Figure 7a). In the density of states diagram (Figure 7b) the situation is mirrored. 

It will be helpful to construct a state diagram from the orbital diagram. 

Figure 9.16. Disrotatory state diagram for butadiene-cyclobutene.

Construct orbital and state diagrams for the following processes ... 

Molerus (1993) developed a state diagram that shows a correlation between these dimensionless groups based on an extremely wide range of data covering 25 < D < 315 mm, 12 < d < 5200/am, and 1270 < ps < 5250 kg/m3 for both hydraulic and pneumatic transport. This state diagram is shown in Fig. 15-3 in the form... 

Figure 15-3 State diagram for suspension transport. (From Molerus, 1993.)...

Figure 18. Additional pressure drop and state diagram for stable conveying particle with sliding strands (e = 0.4). (Wirth andMolerus, 1986.)...

Figure 19. State diagram for suspended flow conveying in horizontal pipes. (Wirth...

Fig. 18. (a) Representation of the tumor hypoxic state (diagram adapted from Ref. (83a). Arrow direction indicates decrease in pC>2 (< 1 mmHg), achieved for tumor depths larger than 100 pm (b) proposed mechanism for redox-mediated retention of [Cu(ATSM)] in hypoxic cells (101-105). Note Contrary to common belief cell membrane crossing solely by direct diffusion is unlikely for compounds of this family is unlikely, as indicated by fluorescence imaging work on aromatic Zn(II) analogs (vide infra). Endocytosis is the more likely uptake mechanism (112-113). 

Fig. 1.19.2. Isoplethal section of the solid-liquid state diagram for R = 0.1. Section fields ...

Shalaev, E. Yu., Kaney, A. N. Study of the solid-liquid state diagram of the water-glycin-suchrose system. Cryobiology, 31, p. 374-382, 1994. Copyright 1994 Academic Press Inc. 

Scheme 20. Transition state diagrams for oxo-imido reactions, illustrating steric effects.

State diagrams are very useful tools in the characterization of amorphous ingredients and food systems (Roos, 1995 Slade and Levine, 1991). Slade and Levine (1988, 1991), acknowledging the earlier work of Franks et al. (1977) and MacKenzie (1977), formulated a state diagram (called a dynamics map or mobility transformation map ) for food systems that includes four dimensions temperature, concentration, pressure, and time. This state... 

State diagrams are an integral part of the food polymer science approach and are further explored and expanded upon in Section III.D.5. For the interested reader, Javenkoski (2001) developed instructional visualization media (three QuickTime animations) for aqueous phase transitions in food systems and investigated their use for improving the comprehension of phase transitions by students enrolled in an introductory food science and human nutrition course. 

Using the time-dependent aspect of state diagrams, Roos (2003) illustrated the effects of temperature, water activity, or water content on relaxation times and relative rates of mechanical changes in amorphous systems (Figure 36). This diagram can be considered as a type of mobility map, where mobility increases (relaxation time decreases) as temperature and/or water content/activity increases. Le Meste et al. (2002) suggested the establishment of mobility maps for food materials showing characteristic relaxation times for different types of molecular motions as a function of temperature and water content. 

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